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paretotails


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statistics: paretotails
Piecewise distribution with generalized Pareto tails.

A paretotails object is a piecewise probability distribution fit to
sample data. A generalized Pareto distribution (GPD) is fit to each tail
of the data, below a lower quantile and above an upper quantile, while the
middle of the distribution is described by the empirical cumulative
distribution function of the data. This gives a smooth model for the
tails, useful for extreme value analysis, together with a nonparametric
description of the central region.

Create a paretotails object with the constructor
pt = paretotails (x, pl, pu), where x
is the sample data and pl and pu are the cumulative
probabilities at the lower and upper tail boundaries. Data at or below the
pl quantile form the lower tail, data at or above the pu
quantile form the upper tail, and the rest form the middle segment.

Query the fitted object with the methods cdf, pdf,
icdf, random, boundary, nsegments,
segment, lowerparams, and upperparams.

Note: the kernel-smoothed middle option of MATLAB
(paretotails (x, pl, pu, "kernel")) is not yet
supported; only the default empirical ("ecdf") middle is available.

See also:
gpfit,
gpcdf,
gppdf,
gpinv,
ecdf,
fitdist,
prob.GeneralizedParetoDistribution


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Piecewise distribution with generalized Pareto tails.



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paretotails.NumParameters


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paretotails: property NumParameters
Number of estimated parameters (two per fitted generalized Pareto tail).


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Number of estimated parameters (two per fitted generalized Pareto tail).



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paretotails.NumSegments


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paretotails: property NumSegments
Number of segments in the piecewise distribution (a lower tail, a middle,
and an upper tail give three).


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Number of segments in the piecewise distribution (a lower tail, a middle, and an upper tail give three).



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paretotails.boundary


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paretotails: [p, q] = boundary (pt)
Boundary probabilities p and quantiles q of the segments of
the paretotails object pt, as column vectors.


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Boundary probabilities p and quantiles q of the segments of the paretotails object pt, as column vectors.



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paretotails.cdf


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paretotails: p = cdf (pt, x)
Cumulative distribution function of the paretotails object
pt evaluated at the values in x.


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Cumulative distribution function of the paretotails object pt evaluated at the values in x.



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paretotails.icdf


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paretotails: x = icdf (pt, p)
Inverse cumulative distribution function (quantile function) of the
paretotails object pt evaluated at the probabilities
p.


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Inverse cumulative distribution function (quantile function) of the paretotails object pt evaluated at the probabilities p.



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paretotails.lowerparams


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paretotails: params = lowerparams (pt)
Shape and scale parameters [k, sigma] of the
generalized Pareto distribution fit to the lower tail of pt.


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Shape and scale parameters [k, sigma] of the generalized Pareto distribution fit to the lower tail of pt.



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paretotails.nsegments


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paretotails: n = nsegments (pt)
Number of segments in the paretotails object pt.


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Number of segments in the paretotails object pt.



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paretotails.paretotails


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paretotails: pt = paretotails (x, pl, pu)
paretotails: pt = paretotails (x, pl, pu, cdffun)
Fit a piecewise distribution with generalized Pareto tails to x.

pl and pu are the cumulative probabilities of the lower and
upper tail boundaries, with 0 <= pl < pu <= 1. A
generalized Pareto distribution is fit by maximum likelihood to the
exceedances in each tail; the middle segment uses the empirical
cumulative distribution of x.

cdffun selects the middle segment and defaults to "ecdf";
the "kernel" option of MATLAB is not yet supported.


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Fit a piecewise distribution with generalized Pareto tails to x.



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paretotails.pdf


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paretotails: y = pdf (pt, x)
Probability density function of the paretotails object pt
evaluated at the values in x.


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Probability density function of the paretotails object pt evaluated at the values in x.



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paretotails.random


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paretotails: r = random (pt)
paretotails: r = random (pt, sz)
paretotails: r = random (pt, m, n, ...)
Random values drawn from the paretotails object pt, by
inverse transform sampling. The size arguments follow rand.


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Random values drawn from the paretotails object pt, by inverse transform sampling.



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paretotails.segment


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paretotails: s = segment (pt, x, p)
Segment indices for the paretotails object pt. Supply the
data values in x (with p empty) or the cumulative
probabilities in p (with x empty). Segment 1 is the
lower tail, 2 the middle, and 3 the upper tail.


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Segment indices for the paretotails object pt.



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paretotails.upperparams


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paretotails: params = upperparams (pt)
Shape and scale parameters [k, sigma] of the
generalized Pareto distribution fit to the upper tail of pt.


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Shape and scale parameters [k, sigma] of the generalized Pareto distribution fit to the upper tail of pt.



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prob.BetaDistribution


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statistics: prob.BetaDistribution
Beta probability distribution object.

A prob.BetaDistribution object consists of parameters, a model
description, and sample data for a beta probability distribution.

The beta distribution is a family of continuous probability distributions
defined on the interval [0, 1] in terms of two positive parameters,
denoted by alpha (a) and beta (b), that appear
as exponents of the variable and its complement to 1, respectively, and
control the shape of the distribution.

There are several ways to create a prob.BetaDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.BetaDistribution (a, b)
to create a beta distribution with fixed parameter values a and
b.
Use the static method prob.BetaDistribution.fit (x,
alpha, freq, options) to fit a distribution to the data
in x using the same input arguments as the betafit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the beta distribution can be found at
https://en.wikipedia.org/wiki/Beta_distribution

See also:
fitdist,
makedist,
betacdf,
betainv,
betapdf,
betarnd,
betafit,
betalike,
betastat


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Beta probability distribution object.



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prob.BetaDistribution.BetaDistribution


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prob.BetaDistribution: pd = BetaDistribution (a, b)
prob.BetaDistribution: pd = BetaDistribution ()
Create a prob.BetaDistribution object.

a and b are the distribution parameters, which the class help
describes. Called with no arguments the parameters take their defaults,
a 1 and b 1.

makedist is the usual way to create a distribution object.


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Create a prob.BetaDistribution object.



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prob.BetaDistribution.DistributionName


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prob.BetaDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


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Probability distribution name



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prob.BetaDistribution.InputData


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prob.BetaDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : an empty array, since prob.BetaDistribution
does not allow censoring.
frequency : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


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Data used for fitting a probability distribution



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prob.BetaDistribution.IsTruncated


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prob.BetaDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


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Flag for truncated probability distribution



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prob.BetaDistribution.NumParameters


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prob.BetaDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


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Number of parameters



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prob.BetaDistribution.ParameterCovariance


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prob.BetaDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 2x2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


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Covariance matrix of the parameter estimates



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prob.BetaDistribution.ParameterDescription


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prob.BetaDistribution: property ParameterDescription
Description of parameters

A 2x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


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Description of parameters



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prob.BetaDistribution.ParameterIsFixed


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prob.BetaDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


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Flag for fixed parameters



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prob.BetaDistribution.ParameterNames


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prob.BetaDistribution: property ParameterNames
Names of parameters

A 2x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
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Names of parameters



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prob.BetaDistribution.ParameterValues


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prob.BetaDistribution: property ParameterValues
Distribution parameter values

A 2x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the a and b
properties.


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Distribution parameter values



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prob.BetaDistribution.Truncation


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prob.BetaDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


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Truncation interval



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prob.BetaDistribution.a


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prob.BetaDistribution: property a
First shape parameter

A positive scalar value characterizing the shape of the beta
distribution. You can access the a property using dot name
assignment.


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First shape parameter



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prob.BetaDistribution.b


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prob.BetaDistribution: property b
Second shape parameter

A positive scalar value characterizing the shape of the beta
distribution. You can access the b property using dot name
assignment.


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Second shape parameter



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prob.BetaDistribution.cdf


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prob.BetaDistribution: p = cdf (pd, x)
prob.BetaDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


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Compute the cumulative distribution function (CDF).



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prob.BetaDistribution.icdf


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prob.BetaDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


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Compute the inverse cumulative distribution function (iCDF).



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prob.BetaDistribution.iqr


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prob.BetaDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


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Compute the interquartile range of a probability distribution.



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prob.BetaDistribution.mean


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prob.BetaDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


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Compute the mean of a probability distribution.



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prob.BetaDistribution.median


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prob.BetaDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


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Compute the median of a probability distribution.



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prob.BetaDistribution.negloglik


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prob.BetaDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood
of the probability distribution object, pd.


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Compute the negative loglikelihood of a probability distribution.



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prob.BetaDistribution.paramci


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prob.BetaDistribution: ci = paramci (pd)
prob.BetaDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


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Compute the confidence intervals for probability distribution parameters.



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prob.BetaDistribution.pdf


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prob.BetaDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


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Compute the probability distribution function (PDF).



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prob.BetaDistribution.plot


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prob.BetaDistribution: plot (pd)
prob.BetaDistribution: plot (pd, Name, Value)
prob.BetaDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


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Plot a probability distribution object.



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prob.BetaDistribution.proflik


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prob.BetaDistribution: [nlogL, param] = proflik (pd, pnum)
prob.BetaDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.BetaDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.BetaDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.BetaDistribution: [nlogL, param] = proflik (pd)
prob.BetaDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the beta distribution, pnum = 1 selects the parameter
a and pnum = 2 selects the parameter b.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


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Profile likelihood function for a probability distribution object.



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prob.BetaDistribution.random


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# elements: 1
# length: 675
prob.BetaDistribution: r = random (pd)
prob.BetaDistribution: r = random (pd, rows)
prob.BetaDistribution: r = random (pd, rows, cols, ...)
prob.BetaDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, betarnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
prob.BetaDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 187
prob.BetaDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.BetaDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 530
prob.BetaDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower,
and upper limit, upper. If pd is fitted to data with
fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
prob.BetaDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 167
prob.BetaDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
prob.BinomialDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1285
statistics: prob.BinomialDistribution
Binomial probability distribution object.

A prob.BinomialDistribution object consists of parameters, a model
description, and sample data for a binomial probability distribution.

The binomial distribution is a discrete probability distribution that
models the number of successes in a sequence of N independent trials,
each with a probability of success p.

There are several ways to create a prob.BinomialDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor
prob.BinomialDistribution (N, p) to create a binomial
distribution with fixed parameter values N and p.
Use the static method prob.BinomialDistribution.fit (x,
ntrials, alpha) to fit a distribution to the data in x
using the same input arguments as the binofit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the binomial distribution can be found at
https://en.wikipedia.org/wiki/Binomial_distribution

See also:
fitdist,
makedist,
binocdf,
binoinv,
binopdf,
binornd,
binofit,
binolike,
binostat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
Binomial probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.BinomialDistribution.BinomialDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 368
prob.BinomialDistribution: pd = BinomialDistribution (N, p)
prob.BinomialDistribution: pd = BinomialDistribution ()
Create a prob.BinomialDistribution object.

N and p are the distribution parameters, which the class help
describes. Called with no arguments the parameters take their defaults,
N 1 and p 0.5.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
Create a prob.BinomialDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.BinomialDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 190
prob.BinomialDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.BinomialDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 576
prob.BinomialDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data : a numeric vector containing the data used for
distribution fitting.
cens : an empty array, since
prob.BinomialDistribution does not allow censoring.
frequency : a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.BinomialDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 210
prob.BinomialDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.BinomialDistribution.N


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 203
prob.BinomialDistribution: property N
Number of trials

A positive integer value characterizing the number of trials in the
binomial distribution. You can access the N property using dot
name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 16
Number of trials



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.BinomialDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 203
prob.BinomialDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.BinomialDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 615
prob.BinomialDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 2x2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.BinomialDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 227
prob.BinomialDistribution: property ParameterDescription
Description of parameters

A 2x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.BinomialDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 283
prob.BinomialDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.BinomialDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 204
prob.BinomialDistribution: property ParameterNames
Names of parameters

A 2x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.BinomialDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 279
prob.BinomialDistribution: property ParameterValues
Distribution parameter values

A 2x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the N and p
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.BinomialDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 347
prob.BinomialDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.BinomialDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 386
prob.BinomialDistribution: p = cdf (pd, x)
prob.BinomialDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.BinomialDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 243
prob.BinomialDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.BinomialDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 193
prob.BinomialDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.BinomialDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 165
prob.BinomialDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.BinomialDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 173
prob.BinomialDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.BinomialDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 219
prob.BinomialDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood
of the probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.BinomialDistribution.p


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 239
prob.BinomialDistribution: property p
Probability of success

A scalar value in the range [0, 1] characterizing the probability
of success in each trial of the binomial distribution. You can access
the p property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 22
Probability of success



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.BinomialDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 977
prob.BinomialDistribution: ci = paramci (pd)
prob.BinomialDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.BinomialDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 203
prob.BinomialDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.BinomialDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1522
prob.BinomialDistribution: plot (pd)
prob.BinomialDistribution: plot (pd, Name, Value)
prob.BinomialDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.BinomialDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2041
prob.BinomialDistribution: [nlogL, param] = proflik (pd, pnum)
prob.BinomialDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.BinomialDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.BinomialDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.BinomialDistribution: [nlogL, param] = proflik (pd)
prob.BinomialDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the binomial distribution, pnum = 1 selects the
parameter N and pnum = 2 selects the parameter
p.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.BinomialDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 691
prob.BinomialDistribution: r = random (pd)
prob.BinomialDistribution: r = random (pd, rows)
prob.BinomialDistribution: r = random (pd, rows, cols, ...)
prob.BinomialDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, binornd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.BinomialDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 191
prob.BinomialDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.BinomialDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 534
prob.BinomialDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower,
and upper limit, upper. If pd is fitted to data with
fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.BinomialDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 171
prob.BinomialDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.BirnbaumSaundersDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1443
statistics: prob.BirnbaumSaundersDistribution
Birnbaum-Saunders probability distribution object.

A prob.BirnbaumSaundersDistribution object consists of parameters, a
model description, and sample data for a Birnbaum-Saunders probability
distribution.

The Birnbaum-Saunders distribution is a continuous probability distribution
that models the time to failure of materials subjected to cyclic loading.
It is defined by scale parameter beta and shape parameter
gamma.

There are several ways to create a prob.BirnbaumSaundersDistribution
object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor
prob.BirnbaumSaundersDistribution (beta, gamma) to
create a Birnbaum-Saunders distribution with fixed parameter values
beta and gamma.
Use the static method prob.BirnbaumSaundersDistribution.fit
(x, alpha, censor, freq, options) to fit a
distribution to the data in x using the same input arguments as the
bisafit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the Birnbaum-Saunders distribution can be found
at
https://en.wikipedia.org/wiki/Birnbaum%E2%80%93Saunders_distribution

See also:
fitdist,
makedist,
bisacdf,
bisainv,
bisapdf,
bisarnd,
bisafit,
bisalike,
bisastat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
Birnbaum-Saunders probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
prob.BirnbaumSaundersDistribution.BirnbaumSaundersDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 427
prob.BirnbaumSaundersDistribution: pd = BirnbaumSaundersDistribution (beta, gamma)
prob.BirnbaumSaundersDistribution: pd = BirnbaumSaundersDistribution ()
Create a prob.BirnbaumSaundersDistribution object.

beta and gamma are the distribution parameters, which the
class help describes. Called with no arguments the parameters take their
defaults, beta 1 and gamma 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
Create a prob.BirnbaumSaundersDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.BirnbaumSaundersDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 198
prob.BirnbaumSaundersDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.BirnbaumSaundersDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 745
prob.BirnbaumSaundersDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.BirnbaumSaundersDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 218
prob.BirnbaumSaundersDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
prob.BirnbaumSaundersDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 211
prob.BirnbaumSaundersDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 53
prob.BirnbaumSaundersDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 624
prob.BirnbaumSaundersDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 2x2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then all elements of the variance-covariance are zero. This
property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 54
prob.BirnbaumSaundersDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 235
prob.BirnbaumSaundersDistribution: property ParameterDescription
Description of parameters

A 2x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.BirnbaumSaundersDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 291
prob.BirnbaumSaundersDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.BirnbaumSaundersDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 212
prob.BirnbaumSaundersDistribution: property ParameterNames
Names of parameters

A 2x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.BirnbaumSaundersDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 294
prob.BirnbaumSaundersDistribution: property ParameterValues
Distribution parameter values

A 2x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the beta and gamma
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.BirnbaumSaundersDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 355
prob.BirnbaumSaundersDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.BirnbaumSaundersDistribution.beta


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 213
prob.BirnbaumSaundersDistribution: property beta
Scale parameter

A positive scalar value characterizing the scale of the
Birnbaum-Saunders distribution. You can access the beta
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.BirnbaumSaundersDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 402
prob.BirnbaumSaundersDistribution: p = cdf (pd, x)
prob.BirnbaumSaundersDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.BirnbaumSaundersDistribution.gamma


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 215
prob.BirnbaumSaundersDistribution: property gamma
Shape parameter

A positive scalar value characterizing the shape of the
Birnbaum-Saunders distribution. You can access the gamma
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Shape parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.BirnbaumSaundersDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 251
prob.BirnbaumSaundersDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.BirnbaumSaundersDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 201
prob.BirnbaumSaundersDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.BirnbaumSaundersDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 173
prob.BirnbaumSaundersDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.BirnbaumSaundersDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 181
prob.BirnbaumSaundersDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.BirnbaumSaundersDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 227
prob.BirnbaumSaundersDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.BirnbaumSaundersDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 993
prob.BirnbaumSaundersDistribution: ci = paramci (pd)
prob.BirnbaumSaundersDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.BirnbaumSaundersDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 211
prob.BirnbaumSaundersDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.BirnbaumSaundersDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1546
prob.BirnbaumSaundersDistribution: plot (pd)
prob.BirnbaumSaundersDistribution: plot (pd, Name, Value)
prob.BirnbaumSaundersDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.BirnbaumSaundersDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2105
prob.BirnbaumSaundersDistribution: [nlogL, param] = proflik (pd, pnum)
prob.BirnbaumSaundersDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.BirnbaumSaundersDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.BirnbaumSaundersDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.BirnbaumSaundersDistribution: [nlogL, param] = proflik (pd)
prob.BirnbaumSaundersDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the Birnbaum-Saunders distribution, pnum = 1 selects
the parameter beta and pnum = 2 selects the
parameter gamma.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.BirnbaumSaundersDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 723
prob.BirnbaumSaundersDistribution: r = random (pd)
prob.BirnbaumSaundersDistribution: r = random (pd, rows)
prob.BirnbaumSaundersDistribution: r = random (pd, rows, cols, ...)
prob.BirnbaumSaundersDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, bisarnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.BirnbaumSaundersDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 199
prob.BirnbaumSaundersDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.BirnbaumSaundersDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 542
prob.BirnbaumSaundersDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower,
and upper limit, upper. If pd is fitted to data with
fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.BirnbaumSaundersDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 179
prob.BirnbaumSaundersDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 21
prob.BurrDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1319
statistics: prob.BurrDistribution
Burr probability distribution object.

A prob.BurrDistribution object consists of parameters, a model
description, and sample data for a Burr probability distribution.

The Burr distribution is a continuous probability distribution that models
a non-negative random variable, commonly used to model household income.
It is defined by a scale parameter alpha and two shape parameters
c and k.

There are several ways to create a prob.BurrDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor
prob.BurrDistribution (alpha, c, k) to create a
Burr distribution with fixed parameter values alpha, c, and
k.
Use the static method prob.BurrDistribution.fit (x,
alpha, censor, freq, options) to fit a
distribution to the data in x using the same input arguments as the
burrfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the Burr distribution can be found at
https://en.wikipedia.org/wiki/Burr_distribution

See also:
fitdist,
makedist,
burrcdf,
burrinv,
burrpdf,
burrrnd,
burrfit,
burrlike,
burrstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
Burr probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.BurrDistribution.BurrDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 369
prob.BurrDistribution: pd = BurrDistribution (alpha, c, k)
prob.BurrDistribution: pd = BurrDistribution ()
Create a prob.BurrDistribution object.

alpha, c and k are the distribution parameters, which
the class help describes. Called with no arguments the parameters take
their defaults, alpha 1, c 1 and k 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
Create a prob.BurrDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.BurrDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 186
prob.BurrDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.BurrDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 560
prob.BurrDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: an empty array, since prob.BurrDistribution
does not allow censoring.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.BurrDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 206
prob.BurrDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.BurrDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 199
prob.BurrDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.BurrDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 612
prob.BurrDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 3x3 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then all elements of the variance-covariance are zero. This
property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.BurrDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 223
prob.BurrDistribution: property ParameterDescription
Description of parameters

A 3x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.BurrDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 279
prob.BurrDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x3 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.BurrDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 200
prob.BurrDistribution: property ParameterNames
Names of parameters

A 3x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.BurrDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 283
prob.BurrDistribution: property ParameterValues
Distribution parameter values

A 3x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the alpha, c, and
k properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.BurrDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 343
prob.BurrDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
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prob.BurrDistribution.alpha


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prob.BurrDistribution: property alpha
Scale parameter

A positive scalar value characterizing the scale of the Burr
distribution. You can access the alpha property using dot name
assignment.


# name: <cell-element>
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Scale parameter



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prob.BurrDistribution.c


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prob.BurrDistribution: property c
First shape parameter

A positive scalar value characterizing the first shape parameter of the
Burr distribution. You can access the c property using dot name
assignment.


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First shape parameter



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prob.BurrDistribution.cdf


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prob.BurrDistribution: p = cdf (pd, x)
prob.BurrDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


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# type: sq_string
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Compute the cumulative distribution function (CDF).



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# length: 26
prob.BurrDistribution.icdf


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# length: 239
prob.BurrDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
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# length: 60
Compute the inverse cumulative distribution function (iCDF).



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# type: sq_string
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# length: 25
prob.BurrDistribution.iqr


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# length: 189
prob.BurrDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


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# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
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# length: 23
prob.BurrDistribution.k


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prob.BurrDistribution: property k
Second shape parameter

A positive scalar value characterizing the second shape parameter of the
Burr distribution. You can access the k property using dot name
assignment.


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Second shape parameter



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# length: 26
prob.BurrDistribution.mean


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prob.BurrDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
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Compute the mean of a probability distribution.



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prob.BurrDistribution.median


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# type: sq_string
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prob.BurrDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


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# length: 49
Compute the median of a probability distribution.



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prob.BurrDistribution.negloglik


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prob.BurrDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


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# length: 65
Compute the negative loglikelihood of a probability distribution.



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# type: sq_string
# elements: 1
# length: 29
prob.BurrDistribution.paramci


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prob.BurrDistribution: ci = paramci (pd)
prob.BurrDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


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Compute the confidence intervals for probability distribution parameters.



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# length: 25
prob.BurrDistribution.pdf


# name: <cell-element>
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# length: 199
prob.BurrDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


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Compute the probability distribution function (PDF).



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prob.BurrDistribution.plot


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prob.BurrDistribution: plot (pd)
prob.BurrDistribution: plot (pd, Name, Value)
prob.BurrDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
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Plot a probability distribution object.



# name: <cell-element>
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prob.BurrDistribution.proflik


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prob.BurrDistribution: [nlogL, param] = proflik (pd, pnum)
prob.BurrDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.BurrDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.BurrDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.BurrDistribution: [nlogL, param] = proflik (pd)
prob.BurrDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the Burr distribution, pnum = 1 selects the parameter
alpha, pnum = 2 selects the parameter c,
and pnum = 3 selects the parameter k.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


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Profile likelihood function for a probability distribution object.



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prob.BurrDistribution.random


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prob.BurrDistribution: r = random (pd)
prob.BurrDistribution: r = random (pd, rows)
prob.BurrDistribution: r = random (pd, rows, cols, ...)
prob.BurrDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, burrrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
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# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
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# length: 25
prob.BurrDistribution.std


# name: <cell-element>
# type: sq_string
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# length: 187
prob.BurrDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


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# length: 61
Compute the standard deviation of a probability distribution.



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# length: 30
prob.BurrDistribution.truncate


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# length: 530
prob.BurrDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower,
and upper limit, upper. If pd is fitted to data with
fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
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# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
prob.BurrDistribution.var


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# type: sq_string
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# length: 167
prob.BurrDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


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# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
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prob.ExponentialDistribution


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statistics: prob.ExponentialDistribution
Exponential probability distribution object.

A prob.ExponentialDistribution object consists of parameters, a
model description, and sample data for a exponential probability
distribution.

The exponential distribution is a continuous probability distribution with
mean parameter mu that models the time between events in a Poisson
process.

There are several ways to create a prob.ExponentialDistribution
object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.ExponentialDistribution (mu)
to create a exponential distribution with fixed parameter value mu.
Use the static method prob.ExponentialDistribution.fit
(x, alpha, censor, freq, options) to fit a
distribution to the data in x using the same input arguments as the
expfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the exponential distribution can be found at
https://en.wikipedia.org/wiki/Exponential_distribution

See also:
fitdist,
makedist,
expcdf,
expinv,
exppdf,
exprnd,
expfit,
explike,
expstat


# name: <cell-element>
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Exponential probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
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prob.ExponentialDistribution.DistributionName


# name: <cell-element>
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# length: 193
prob.ExponentialDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
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Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
prob.ExponentialDistribution.ExponentialDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 362
prob.ExponentialDistribution: pd = ExponentialDistribution (mu)
prob.ExponentialDistribution: pd = ExponentialDistribution ()
Create a prob.ExponentialDistribution object.

mu is the distribution parameter, which the class help describes.
Called with no arguments the parameter takes its default, mu 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
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Create a prob.ExponentialDistribution object.



# name: <cell-element>
# type: sq_string
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# length: 38
prob.ExponentialDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 740
prob.ExponentialDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
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Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.ExponentialDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
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prob.ExponentialDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
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# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.ExponentialDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 206
prob.ExponentialDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.ExponentialDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
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# length: 453
prob.ExponentialDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A scalar numeric value containing the variance-covariance of the
parameter estimate. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then the variance-covariance is zero. This
property is read-only.


# name: <cell-element>
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Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.ExponentialDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
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# length: 230
prob.ExponentialDistribution: property ParameterDescription
Description of parameters

A 1x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.ExponentialDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 277
prob.ExponentialDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x1 logical vector specifying whether the parameter is fixed or
estimated. true value corresponds to fixed parameter,
false value corresponds to parameter estimate. This property is
read-only.


# name: <cell-element>
# type: sq_string
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# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.ExponentialDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 207
prob.ExponentialDistribution: property ParameterNames
Names of parameters

A 1x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.ExponentialDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 273
prob.ExponentialDistribution: property ParameterValues
Distribution parameter values

A 1x1 numeric vector containing the value of the distribution
parameter. This property is read-only. You can change the distribution
parameter by assigning a new value to the mu
property.


# name: <cell-element>
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# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.ExponentialDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 350
prob.ExponentialDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.ExponentialDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 392
prob.ExponentialDistribution: p = cdf (pd, x)
prob.ExponentialDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.ExponentialDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 246
prob.ExponentialDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.ExponentialDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 196
prob.ExponentialDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.ExponentialDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 168
prob.ExponentialDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.ExponentialDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 176
prob.ExponentialDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.ExponentialDistribution.mu


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 196
prob.ExponentialDistribution: property mu
Mean parameter

A positive scalar value characterizing the mean of the
exponential distribution. You can access the mu
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 14
Mean parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.ExponentialDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 222
prob.ExponentialDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.ExponentialDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 983
prob.ExponentialDistribution: ci = paramci (pd)
prob.ExponentialDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


# name: <cell-element>
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# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.ExponentialDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 206
prob.ExponentialDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
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Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.ExponentialDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1531
prob.ExponentialDistribution: plot (pd)
prob.ExponentialDistribution: plot (pd, Name, Value)
prob.ExponentialDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.ExponentialDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2026
prob.ExponentialDistribution: [nlogL, param] = proflik (pd, pnum)
prob.ExponentialDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.ExponentialDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.ExponentialDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.ExponentialDistribution: [nlogL, param] = proflik (pd)
prob.ExponentialDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the exponential distribution, pnum = 1 selects the
parameter mu.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.ExponentialDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 703
prob.ExponentialDistribution: r = random (pd)
prob.ExponentialDistribution: r = random (pd, rows)
prob.ExponentialDistribution: r = random (pd, rows, cols, ...)
prob.ExponentialDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, betarnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.ExponentialDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 194
prob.ExponentialDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.ExponentialDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 537
prob.ExponentialDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower,
and upper limit, upper. If pd is fitted to data with
fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.ExponentialDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 174
prob.ExponentialDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.ExtremeValueDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1399
statistics: prob.ExtremeValueDistribution
Extreme value probability distribution object.

A prob.ExtremeValueDistribution object consists of parameters, a
model description, and sample data for an extreme value probability
distribution.

The extreme value distribution is also known as the Gumbel distribution for
maxima, and it is a limiting distribution for the maximum of a large number
of samples from a continuous distribution. It is defined by location
parameter mu and scale parameter sigma.

There are several ways to create a prob.ExtremeValueDistribution
object.

Fit a distribution to data using the fitdist function.
Create a distribution with specified parameter values using the
makedist function.
Use the constructor prob.ExtremeValueDistribution (mu,
sigma) to create an extreme value distribution with specified
parameter values.
Use the static method prob.ExtremeValueDistribution.fit
(x, alpha, censor, freq, options) to fit a
distribution to the data in x using the same input arguments as the
evfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the
constructor and the aforementioned static method.

Further information about the Gumbel distribution can be found at
https://en.wikipedia.org/wiki/Gumbel_distribution

See also:
fitdist,
makedist,
evcdf,
evinv,
evpdf,
evrnd,
evfit,
evlike,
evstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
Extreme value probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.ExtremeValueDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 194
prob.ExtremeValueDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 54
prob.ExtremeValueDistribution.ExtremeValueDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 401
prob.ExtremeValueDistribution: pd = ExtremeValueDistribution (mu, sigma)
prob.ExtremeValueDistribution: pd = ExtremeValueDistribution ()
Create a prob.ExtremeValueDistribution object.

mu and sigma are the distribution parameters, which the class
help describes. Called with no arguments the parameters take their
defaults, mu 0 and sigma 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
Create a prob.ExtremeValueDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.ExtremeValueDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 741
prob.ExtremeValueDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.ExtremeValueDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 214
prob.ExtremeValueDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.ExtremeValueDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 207
prob.ExtremeValueDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.ExtremeValueDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 620
prob.ExtremeValueDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 2x2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then all elements of the variance-covariance are zero. This
property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.ExtremeValueDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 231
prob.ExtremeValueDistribution: property ParameterDescription
Description of parameters

A 2x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.ExtremeValueDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 287
prob.ExtremeValueDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.ExtremeValueDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 208
prob.ExtremeValueDistribution: property ParameterNames
Names of parameters

A 2x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.ExtremeValueDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 288
prob.ExtremeValueDistribution: property ParameterValues
Distribution parameter values

A 2x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the mu and sigma
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.ExtremeValueDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 351
prob.ExtremeValueDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.ExtremeValueDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 394
prob.ExtremeValueDistribution: p = cdf (pd, x)
prob.ExtremeValueDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.ExtremeValueDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 247
prob.ExtremeValueDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.ExtremeValueDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 197
prob.ExtremeValueDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.ExtremeValueDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 169
prob.ExtremeValueDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.ExtremeValueDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 177
prob.ExtremeValueDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.ExtremeValueDistribution.mu


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 198
prob.ExtremeValueDistribution: property mu
Location parameter

A scalar value characterizing the location of the
extreme value distribution. You can access the mu
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
Location parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.ExtremeValueDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 223
prob.ExtremeValueDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.ExtremeValueDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 985
prob.ExtremeValueDistribution: ci = paramci (pd)
prob.ExtremeValueDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.ExtremeValueDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 207
prob.ExtremeValueDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.ExtremeValueDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1534
prob.ExtremeValueDistribution: plot (pd)
prob.ExtremeValueDistribution: plot (pd, Name, Value)
prob.ExtremeValueDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.ExtremeValueDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2075
prob.ExtremeValueDistribution: [nlogL, param] = proflik (pd, pnum)
prob.ExtremeValueDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.ExtremeValueDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.ExtremeValueDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.ExtremeValueDistribution: [nlogL, param] = proflik (pd)
prob.ExtremeValueDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the extreme value distribution, pnum = 1 selects the
parameter mu and pnum = 2 selects the parameter
sigma.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.ExtremeValueDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 707
prob.ExtremeValueDistribution: r = random (pd)
prob.ExtremeValueDistribution: r = random (pd, rows)
prob.ExtremeValueDistribution: r = random (pd, rows, cols, ...)
prob.ExtremeValueDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, betarnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.ExtremeValueDistribution.sigma


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 207
prob.ExtremeValueDistribution: property sigma
Scale parameter

A positive scalar value characterizing the scale of the
extreme value distribution. You can access the sigma
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.ExtremeValueDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 195
prob.ExtremeValueDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.ExtremeValueDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 538
prob.ExtremeValueDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower,
and upper limit, upper. If pd is fitted to data with
fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.ExtremeValueDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 175
prob.ExtremeValueDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 22
prob.GammaDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1251
statistics: prob.GammaDistribution
Gamma probability distribution object.

A prob.GammaDistribution object consists of parameters, a model
description, and sample data for a gamma probability distribution.

The gamma distribution is a continuous probability distribution that models
the time to failure of a process. It is defined by shape parameter a
and scale parameter b.

There are several ways to create a prob.GammaDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.GammaDistribution (a, b)
to create a gamma distribution with fixed parameter values a and
b.
Use the static method prob.GammaDistribution.fit (x,
alpha, censor, freq, options) to fit a
distribution to the data in x using the same input arguments as the
gamfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the gamma distribution can be found at
https://en.wikipedia.org/wiki/Gamma_distribution

See also:
fitdist,
makedist,
gamcdf,
gaminv,
gampdf,
gamrnd,
gamfit,
gamlike,
gamstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
Gamma probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.GammaDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 187
prob.GammaDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.GammaDistribution.GammaDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 351
prob.GammaDistribution: pd = GammaDistribution (a, b)
prob.GammaDistribution: pd = GammaDistribution ()
Create a prob.GammaDistribution object.

a and b are the distribution parameters, which the class help
describes. Called with no arguments the parameters take their defaults,
a 1 and b 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Create a prob.GammaDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.GammaDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 734
prob.GammaDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.GammaDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 207
prob.GammaDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.GammaDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 200
prob.GammaDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.GammaDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 613
prob.GammaDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 2x2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then all elements of the variance-covariance are zero. This
property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.GammaDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 224
prob.GammaDistribution: property ParameterDescription
Description of parameters

A 2x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.GammaDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 280
prob.GammaDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.GammaDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 201
prob.GammaDistribution: property ParameterNames
Names of parameters

A 2x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.GammaDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 276
prob.GammaDistribution: property ParameterValues
Distribution parameter values

A 2x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the a and b
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.GammaDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 344
prob.GammaDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 24
prob.GammaDistribution.a


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 184
prob.GammaDistribution: property a
Shape parameter

A positive scalar value characterizing the shape of the
gamma distribution. You can access the a
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Shape parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 24
prob.GammaDistribution.b


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 184
prob.GammaDistribution: property b
Scale parameter

A positive scalar value characterizing the scale of the
gamma distribution. You can access the b
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.GammaDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 380
prob.GammaDistribution: p = cdf (pd, x)
prob.GammaDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.GammaDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 240
prob.GammaDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.GammaDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 190
prob.GammaDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.GammaDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 162
prob.GammaDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.GammaDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 170
prob.GammaDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.GammaDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 216
prob.GammaDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.GammaDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 971
prob.GammaDistribution: ci = paramci (pd)
prob.GammaDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.GammaDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 200
prob.GammaDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.GammaDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1513
prob.GammaDistribution: plot (pd)
prob.GammaDistribution: plot (pd, Name, Value)
prob.GammaDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.GammaDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2020
prob.GammaDistribution: [nlogL, param] = proflik (pd, pnum)
prob.GammaDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.GammaDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.GammaDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.GammaDistribution: [nlogL, param] = proflik (pd)
prob.GammaDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the gamma distribution, pnum = 1 selects the parameter
a and pnum = 2 selects the parameter b.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.GammaDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 678
prob.GammaDistribution: r = random (pd)
prob.GammaDistribution: r = random (pd, rows)
prob.GammaDistribution: r = random (pd, rows, cols, ...)
prob.GammaDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, gamrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.GammaDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 188
prob.GammaDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.GammaDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 531
prob.GammaDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower,
and upper limit, upper. If pd is fitted to data with
fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.GammaDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 168
prob.GammaDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.GeneralizedExtremeValueDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1480
statistics: prob.GeneralizedExtremeValueDistribution
Generalized extreme value probability distribution object.

A prob.GeneralizedExtremeValueDistribution object consists of
parameters, a model description, and sample data for a generalized extreme
value probability distribution.

The generalized extreme value distribution is a continuous probability
distribution that models extreme values. It is defined by shape parameter
k, scale parameter sigma, and location parameter mu.

There are several ways to create a
prob.GeneralizedExtremeValueDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.GeneralizedExtremeValueDistribution
(k, sigma, mu) to create a generalized extreme value
distribution with fixed parameter values k, sigma, and
mu.
Use the static method
prob.GeneralizedExtremeValueDistribution.fit (x, alpha,
freq, options) to fit a distribution to the data in x
using the same input arguments as the gevfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the generalized extreme value distribution can be
found at
https://en.wikipedia.org/wiki/Generalized_extreme_value_distribution

See also:
fitdist,
makedist,
gevcdf,
gevinv,
gevpdf,
gevrnd,
gevfit,
gevlike,
gevstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 58
Generalized extreme value probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 57
prob.GeneralizedExtremeValueDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 205
prob.GeneralizedExtremeValueDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 76
prob.GeneralizedExtremeValueDistribution.GeneralizedExtremeValueDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 467
prob.GeneralizedExtremeValueDistribution: pd = GeneralizedExtremeValueDistribution (k, sigma, mu)
prob.GeneralizedExtremeValueDistribution: pd = GeneralizedExtremeValueDistribution ()
Create a prob.GeneralizedExtremeValueDistribution object.

k, sigma and mu are the distribution parameters, which
the class help describes. Called with no arguments the parameters take
their defaults, k 0, sigma 1 and mu 0.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 57
Create a prob.GeneralizedExtremeValueDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.GeneralizedExtremeValueDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 752
prob.GeneralizedExtremeValueDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
prob.GeneralizedExtremeValueDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 225
prob.GeneralizedExtremeValueDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 54
prob.GeneralizedExtremeValueDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 218
prob.GeneralizedExtremeValueDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
prob.GeneralizedExtremeValueDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 631
prob.GeneralizedExtremeValueDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 3x3 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then all elements of the variance-covariance are zero. This
property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
prob.GeneralizedExtremeValueDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 242
prob.GeneralizedExtremeValueDistribution: property ParameterDescription
Description of parameters

A 3x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 57
prob.GeneralizedExtremeValueDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 298
prob.GeneralizedExtremeValueDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x3 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 55
prob.GeneralizedExtremeValueDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 219
prob.GeneralizedExtremeValueDistribution: property ParameterNames
Names of parameters

A 3x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 56
prob.GeneralizedExtremeValueDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 303
prob.GeneralizedExtremeValueDistribution: property ParameterValues
Distribution parameter values

A 3x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the k, sigma, and
mu properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
prob.GeneralizedExtremeValueDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 362
prob.GeneralizedExtremeValueDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.GeneralizedExtremeValueDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 416
prob.GeneralizedExtremeValueDistribution: p = cdf (pd, x)
prob.GeneralizedExtremeValueDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.GeneralizedExtremeValueDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 258
prob.GeneralizedExtremeValueDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.GeneralizedExtremeValueDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 208
prob.GeneralizedExtremeValueDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.GeneralizedExtremeValueDistribution.k


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 213
prob.GeneralizedExtremeValueDistribution: property k
Shape parameter

A scalar value characterizing the shape of the generalized extreme value
distribution. You can access the k property using dot name
assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Shape parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.GeneralizedExtremeValueDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 180
prob.GeneralizedExtremeValueDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
prob.GeneralizedExtremeValueDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 188
prob.GeneralizedExtremeValueDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.GeneralizedExtremeValueDistribution.mu


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 221
prob.GeneralizedExtremeValueDistribution: property mu
Location parameter

A scalar value characterizing the location of the generalized extreme
value distribution. You can access the mu property using dot name
assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
Location parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.GeneralizedExtremeValueDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 234
prob.GeneralizedExtremeValueDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.GeneralizedExtremeValueDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1007
prob.GeneralizedExtremeValueDistribution: ci = paramci (pd)
prob.GeneralizedExtremeValueDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.GeneralizedExtremeValueDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 218
prob.GeneralizedExtremeValueDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.GeneralizedExtremeValueDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1567
prob.GeneralizedExtremeValueDistribution: plot (pd)
prob.GeneralizedExtremeValueDistribution: plot (pd, Name, Value)
prob.GeneralizedExtremeValueDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.GeneralizedExtremeValueDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2188
prob.GeneralizedExtremeValueDistribution: [nlogL, param] = proflik (pd, pnum)
prob.GeneralizedExtremeValueDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.GeneralizedExtremeValueDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.GeneralizedExtremeValueDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.GeneralizedExtremeValueDistribution: [nlogL, param] = proflik (pd)
prob.GeneralizedExtremeValueDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the generalized extreme value distribution, pnum = 1
selects the parameter k, pnum = 2 selects the
parameter sigma, and pnum = 3 selects the
parameter mu.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
prob.GeneralizedExtremeValueDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 750
prob.GeneralizedExtremeValueDistribution: r = random (pd)
prob.GeneralizedExtremeValueDistribution: r = random (pd, rows)
prob.GeneralizedExtremeValueDistribution: r = random (pd, rows, cols, ...)
prob.GeneralizedExtremeValueDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, gevrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.GeneralizedExtremeValueDistribution.sigma


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 230
prob.GeneralizedExtremeValueDistribution: property sigma
Scale parameter

A positive scalar value characterizing the scale of the generalized
extreme value distribution. You can access the sigma property
using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.GeneralizedExtremeValueDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 206
prob.GeneralizedExtremeValueDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.GeneralizedExtremeValueDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 549
prob.GeneralizedExtremeValueDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower,
and upper limit, upper. If pd is fitted to data with
fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.GeneralizedExtremeValueDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 186
prob.GeneralizedExtremeValueDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.GeneralizedParetoDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1484
statistics: prob.GeneralizedParetoDistribution
Generalized Pareto probability distribution object.

A prob.GeneralizedParetoDistribution object consists of parameters,
a model description, and sample data for a Generalized Pareto probability
distribution.

The Generalized Pareto distribution is a continuous probability
distribution that models the tail behavior of other distributions, commonly
used for extreme value analysis. It is defined by shape parameter k,
scale parameter sigma, and location parameter theta.

There are several ways to create a
prob.GeneralizedParetoDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.GeneralizedParetoDistribution
(k, sigma, theta) to create a Generalized Pareto
distribution with fixed parameter values k, sigma, and
theta.
Use the static method prob.GeneralizedParetoDistribution.fit
(x, theta, alpha, freq, options) to fit a
distribution to the data in x using the same input arguments as the
gpfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the Generalized Pareto distribution can be found
at
https://en.wikipedia.org/wiki/Generalized_Pareto_distribution

See also:
fitdist,
makedist,
gpcdf,
gpinv,
gppdf,
gprnd,
gpfit,
gplike,
gpstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Generalized Pareto probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
prob.GeneralizedParetoDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 199
prob.GeneralizedParetoDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
prob.GeneralizedParetoDistribution.GeneralizedParetoDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 446
prob.GeneralizedParetoDistribution: pd = GeneralizedParetoDistribution (k, sigma, theta)
prob.GeneralizedParetoDistribution: pd = GeneralizedParetoDistribution ()
Create a prob.GeneralizedParetoDistribution object.

k, sigma and theta are the distribution parameters,
which the class help describes. Called with no arguments the parameters
take their defaults, k 1, sigma 1 and theta 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Create a prob.GeneralizedParetoDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.GeneralizedParetoDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 746
prob.GeneralizedParetoDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.GeneralizedParetoDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 219
prob.GeneralizedParetoDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.GeneralizedParetoDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 212
prob.GeneralizedParetoDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 54
prob.GeneralizedParetoDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 625
prob.GeneralizedParetoDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 3x3 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then all elements of the variance-covariance are zero. This
property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 55
prob.GeneralizedParetoDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 236
prob.GeneralizedParetoDistribution: property ParameterDescription
Description of parameters

A 3x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
prob.GeneralizedParetoDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 292
prob.GeneralizedParetoDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x3 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.GeneralizedParetoDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 213
prob.GeneralizedParetoDistribution: property ParameterNames
Names of parameters

A 3x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.GeneralizedParetoDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 300
prob.GeneralizedParetoDistribution: property ParameterValues
Distribution parameter values

A 3x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the k, sigma, and
theta properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.GeneralizedParetoDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 356
prob.GeneralizedParetoDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.GeneralizedParetoDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 404
prob.GeneralizedParetoDistribution: p = cdf (pd, x)
prob.GeneralizedParetoDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.GeneralizedParetoDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 252
prob.GeneralizedParetoDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.GeneralizedParetoDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 202
prob.GeneralizedParetoDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.GeneralizedParetoDistribution.k


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 200
prob.GeneralizedParetoDistribution: property k
Shape parameter

A scalar value characterizing the shape of the Generalized Pareto
distribution. You can access the k property using dot name
assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Shape parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.GeneralizedParetoDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 174
prob.GeneralizedParetoDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.GeneralizedParetoDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 182
prob.GeneralizedParetoDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.GeneralizedParetoDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 228
prob.GeneralizedParetoDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.GeneralizedParetoDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 995
prob.GeneralizedParetoDistribution: ci = paramci (pd)
prob.GeneralizedParetoDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.GeneralizedParetoDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 212
prob.GeneralizedParetoDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.GeneralizedParetoDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1549
prob.GeneralizedParetoDistribution: plot (pd)
prob.GeneralizedParetoDistribution: plot (pd, Name, Value)
prob.GeneralizedParetoDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.GeneralizedParetoDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2148
prob.GeneralizedParetoDistribution: [nlogL, param] = proflik (pd, pnum)
prob.GeneralizedParetoDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.GeneralizedParetoDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.GeneralizedParetoDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.GeneralizedParetoDistribution: [nlogL, param] = proflik (pd)
prob.GeneralizedParetoDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the Generalized Pareto distribution, pnum = 1 selects
the parameter k, pnum = 2 selects the parameter
sigma, and pnum = 3 selects the parameter
theta.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.GeneralizedParetoDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 726
prob.GeneralizedParetoDistribution: r = random (pd)
prob.GeneralizedParetoDistribution: r = random (pd, rows)
prob.GeneralizedParetoDistribution: r = random (pd, rows, cols, ...)
prob.GeneralizedParetoDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, random returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.GeneralizedParetoDistribution.sigma


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 217
prob.GeneralizedParetoDistribution: property sigma
Scale parameter

A positive scalar value characterizing the scale of the Generalized
Pareto distribution. You can access the sigma property using dot
name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.GeneralizedParetoDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 200
prob.GeneralizedParetoDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.GeneralizedParetoDistribution.theta


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 214
prob.GeneralizedParetoDistribution: property theta
Location parameter

A scalar value characterizing the location of the Generalized Pareto
distribution. You can access the theta property using dot name
assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
Location parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.GeneralizedParetoDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 543
prob.GeneralizedParetoDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower,
and upper limit, upper. If pd is fitted to data with
fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.GeneralizedParetoDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 180
prob.GeneralizedParetoDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.HalfNormalDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1330
statistics: prob.HalfNormalDistribution
Half-normal probability distribution object.

A prob.HalfNormalDistribution object consists of parameters, a model
description, and sample data for a half-normal probability distribution.

The half-normal distribution is a continuous probability distribution that
models the time to failure of materials subjected to cyclic loading. It is
defined by location parameter mu and scale parameter sigma.

There are several ways to create a prob.HalfNormalDistribution
object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.HalfNormalDistribution (mu,
sigma) to create a half-normal distribution with fixed parameter
values mu and sigma.
Use the static method
prob.HalfNormalDistribution.fit (x, mu, freq) to
fit a distribution to the data in x using the same input arguments as
the hnfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the half-normal distribution can be found at
https://en.wikipedia.org/wiki/Half-normal_distribution

See also:
fitdist,
makedist,
hncdf,
hninv,
hnpdf,
hnrnd,
hnfit,
hnlike,
hnstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Half-normal probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.HalfNormalDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 192
prob.HalfNormalDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.HalfNormalDistribution.HalfNormalDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 391
prob.HalfNormalDistribution: pd = HalfNormalDistribution (mu, sigma)
prob.HalfNormalDistribution: pd = HalfNormalDistribution ()
Create a prob.HalfNormalDistribution object.

mu and sigma are the distribution parameters, which the class
help describes. Called with no arguments the parameters take their
defaults, mu 0 and sigma 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Create a prob.HalfNormalDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.HalfNormalDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 739
prob.HalfNormalDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.HalfNormalDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 212
prob.HalfNormalDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.HalfNormalDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 205
prob.HalfNormalDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
prob.HalfNormalDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 618
prob.HalfNormalDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 2x2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.HalfNormalDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 229
prob.HalfNormalDistribution: property ParameterDescription
Description of parameters

A 2x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.HalfNormalDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 285
prob.HalfNormalDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.HalfNormalDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 206
prob.HalfNormalDistribution: property ParameterNames
Names of parameters

A 2x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.HalfNormalDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 286
prob.HalfNormalDistribution: property ParameterValues
Distribution parameter values

A 2x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the mu and sigma
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.HalfNormalDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 349
prob.HalfNormalDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.HalfNormalDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 390
prob.HalfNormalDistribution: p = cdf (pd, x)
prob.HalfNormalDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.HalfNormalDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 245
prob.HalfNormalDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.HalfNormalDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 195
prob.HalfNormalDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.HalfNormalDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 167
prob.HalfNormalDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.HalfNormalDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 175
prob.HalfNormalDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.HalfNormalDistribution.mu


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 194
prob.HalfNormalDistribution: property mu
Location parameter

A scalar value characterizing the location of the
half-normal distribution. You can access the mu
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
Location parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.HalfNormalDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 221
prob.HalfNormalDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.HalfNormalDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 981
prob.HalfNormalDistribution: ci = paramci (pd)
prob.HalfNormalDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.HalfNormalDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 205
prob.HalfNormalDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
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prob.HalfNormalDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1528
prob.HalfNormalDistribution: plot (pd)
prob.HalfNormalDistribution: plot (pd, Name, Value)
prob.HalfNormalDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
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Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.HalfNormalDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2061
prob.HalfNormalDistribution: [nlogL, param] = proflik (pd, pnum)
prob.HalfNormalDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.HalfNormalDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.HalfNormalDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.HalfNormalDistribution: [nlogL, param] = proflik (pd)
prob.HalfNormalDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the Half-normal distribution, pnum = 1 selects
the parameter mu and pnum = 2 selects the
parameter sigma.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
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Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.HalfNormalDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 697
prob.HalfNormalDistribution: r = random (pd)
prob.HalfNormalDistribution: r = random (pd, rows)
prob.HalfNormalDistribution: r = random (pd, rows, cols, ...)
prob.HalfNormalDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, hnrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.HalfNormalDistribution.sigma


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 203
prob.HalfNormalDistribution: property sigma
Scale parameter

A positive scalar value characterizing the scale of the
half-normal distribution. You can access the sigma
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.HalfNormalDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 193
prob.HalfNormalDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.HalfNormalDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 536
prob.HalfNormalDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower, and upper limit, upper. If pd is fitted to data
with fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.HalfNormalDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 173
prob.HalfNormalDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.InverseGaussianDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1413
statistics: prob.InverseGaussianDistribution
Inverse Gaussian probability distribution object.

A prob.InverseGaussianDistribution object consists of parameters, a
model description, and sample data for a Inverse Gaussian probability
distribution.

The Inverse Gaussian distribution is a continuous probability distribution,
which is often used to model non-negative positively skewed data. Is is
defined by mean parameter mu and shape parameter lambda.

There are several ways to create a prob.InverseGaussianDistribution
object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor
prob.InverseGaussianDistribution (mu, lambda) to create
a Inverse Gaussian distribution with fixed parameter values mu and
lambda.
Use the static method prob.InverseGaussianDistribution.fit
(x, alpha, censor, freq, options) to fit a
distribution to the data in x using the same input arguments as the
invgfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the Inverse Gaussian distribution can be found at
https://en.wikipedia.org/wiki/Inverse_Gaussian_distribution

See also:
fitdist,
makedist,
invgcdf,
invginv,
invgpdf,
invgrnd,
invgfit,
invglike,
invgstat


# name: <cell-element>
# type: sq_string
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# length: 49
Inverse Gaussian probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.InverseGaussianDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 197
prob.InverseGaussianDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.InverseGaussianDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 744
prob.InverseGaussianDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
prob.InverseGaussianDistribution.InverseGaussianDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 419
prob.InverseGaussianDistribution: pd = InverseGaussianDistribution (mu, lambda)
prob.InverseGaussianDistribution: pd = InverseGaussianDistribution ()
Create a prob.InverseGaussianDistribution object.

mu and lambda are the distribution parameters, which the
class help describes. Called with no arguments the parameters take their
defaults, mu 1 and lambda 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Create a prob.InverseGaussianDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.InverseGaussianDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 217
prob.InverseGaussianDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.InverseGaussianDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 210
prob.InverseGaussianDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
prob.InverseGaussianDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 623
prob.InverseGaussianDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 2x2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then all elements of the variance-covariance are zero. This
property is read-only.


# name: <cell-element>
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# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 53
prob.InverseGaussianDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 234
prob.InverseGaussianDistribution: property ParameterDescription
Description of parameters

A 2x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.InverseGaussianDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 290
prob.InverseGaussianDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
prob.InverseGaussianDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 211
prob.InverseGaussianDistribution: property ParameterNames
Names of parameters

A 2x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.InverseGaussianDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 292
prob.InverseGaussianDistribution: property ParameterValues
Distribution parameter values

A 2x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the mu and lambda
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.InverseGaussianDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 354
prob.InverseGaussianDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.InverseGaussianDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 400
prob.InverseGaussianDistribution: p = cdf (pd, x)
prob.InverseGaussianDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
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Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.InverseGaussianDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 250
prob.InverseGaussianDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.InverseGaussianDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 200
prob.InverseGaussianDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.InverseGaussianDistribution.lambda


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 215
prob.InverseGaussianDistribution: property lambda
Shape parameter

A positive scalar value characterizing the shape of the
Inverse Gaussian distribution. You can access the lambda
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Shape parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.InverseGaussianDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 172
prob.InverseGaussianDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.InverseGaussianDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 180
prob.InverseGaussianDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.InverseGaussianDistribution.mu


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 205
prob.InverseGaussianDistribution: property mu
Mean parameter

A positive scalar value characterizing the mean of the
Inverse Gaussian distribution. You can access the mu
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 14
Mean parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.InverseGaussianDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 226
prob.InverseGaussianDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.InverseGaussianDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 991
prob.InverseGaussianDistribution: ci = paramci (pd)
prob.InverseGaussianDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.InverseGaussianDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 210
prob.InverseGaussianDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.InverseGaussianDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1543
prob.InverseGaussianDistribution: plot (pd)
prob.InverseGaussianDistribution: plot (pd, Name, Value)
prob.InverseGaussianDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.InverseGaussianDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2097
prob.InverseGaussianDistribution: [nlogL, param] = proflik (pd, pnum)
prob.InverseGaussianDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.InverseGaussianDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.InverseGaussianDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.InverseGaussianDistribution: [nlogL, param] = proflik (pd)
prob.InverseGaussianDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the Inverse Gaussian distribution, pnum = 1 selects
the parameter mu and pnum = 2 selects the
parameter lambda.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.InverseGaussianDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 719
prob.InverseGaussianDistribution: r = random (pd)
prob.InverseGaussianDistribution: r = random (pd, rows)
prob.InverseGaussianDistribution: r = random (pd, rows, cols, ...)
prob.InverseGaussianDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, invgrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.InverseGaussianDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 198
prob.InverseGaussianDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.InverseGaussianDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 541
prob.InverseGaussianDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower,
and upper limit, upper. If pd is fitted to data with
fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.InverseGaussianDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 178
prob.InverseGaussianDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 23
prob.KernelDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 839
statistics: prob.KernelDistribution
Kernel probability distribution object.

A prob.KernelDistribution object consists of a nonparametric kernel
smoothing density estimate fitted to sample data, together with a model
description. Unlike the parametric distribution objects, it has no
estimated parameters; the fitted distribution is defined entirely by the
data, the smoothing kernel, and the bandwidth.

A prob.KernelDistribution object can only be created by fitting a
kernel smoothing distribution to data with the fitdist function.
Unlike the parametric distributions, it cannot be created with the
makedist function, since it is not parametric and requires data.

Further information about the kernel density estimation can be found at
https://en.wikipedia.org/wiki/Kernel_density_estimation

See also:
fitdist,
ksdensity,
mvksdensity


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Kernel probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.KernelDistribution.Bandwidth


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 217
prob.KernelDistribution: property Bandwidth
Bandwidth of the smoothing kernel

A positive scalar value specifying the bandwidth of the smoothing kernel.
You can access the Bandwidth property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
Bandwidth of the smoothing kernel



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.KernelDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 188
prob.KernelDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.KernelDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 568
prob.KernelDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: an empty array, since censoring is not supported for
a kernel distribution.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.KernelDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 208
prob.KernelDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.KernelDistribution.Kernel


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 280
prob.KernelDistribution: property Kernel
Kernel smoothing function

A character vector specifying the type of smoothing kernel used for the
density estimate. It is one of 'normal', 'box',
'triangle', or 'epanechnikov'. You can access the
Kernel property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Kernel smoothing function



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.KernelDistribution.KernelDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 469
prob.KernelDistribution: pd = KernelDistribution (data, kernel, bw, support, freq)
prob.KernelDistribution: pd = KernelDistribution ()
Create a prob.KernelDistribution object.

data, kernel, bw, support and freq are the
distribution parameters, which the class help describes. Called with no
arguments it fits the data [0; 1] with a normal kernel over an
unbounded support, taking the bandwidth from the data.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
Create a prob.KernelDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.KernelDistribution.Support


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 467
prob.KernelDistribution: property Support
Support of the probability distribution

A scalar structure containing the following fields:

range: either the character vector 'unbounded' or
'positive', or a two-element numeric vector [L, U] with
the lower and upper bounds of the support.
closedbound: a two-element logical vector specifying
whether each bound is closed.
iscontinuous: a logical scalar, always true for a
kernel distribution.

This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Support of the probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.KernelDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 345
prob.KernelDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.KernelDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 464
prob.KernelDistribution: p = cdf (pd, x)
prob.KernelDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.

x must be double or single; integer, logical, and
character arrays are rejected.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.KernelDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 323
prob.KernelDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.

p must be double or single; integer, logical, and
character arrays are rejected.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.KernelDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 191
prob.KernelDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.KernelDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 163
prob.KernelDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.KernelDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 171
prob.KernelDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.KernelDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 217
prob.KernelDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.KernelDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 278
prob.KernelDistribution: y = pdf (pd, x)
Compute the probability density function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.

x must be double or single; integer, logical, and
character arrays are rejected.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the probability density function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.KernelDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1008
prob.KernelDistribution: plot (pd)
prob.KernelDistribution: plot (pd, Name, Value)
prob.KernelDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd, superimposed over a histogram
of the data used to fit it.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF)
superimposed on a histogram of the data. 'cdf' plots the
cumulative distribution function (CDF) superimposed over an empirical
CDF. 'probability' plots a probability plot using a CDF of the
data and a CDF of the fitted probability distribution.
'Parent' An axes graphics object for plot. If not
specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.KernelDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 682
prob.KernelDistribution: r = random (pd)
prob.KernelDistribution: r = random (pd, rows)
prob.KernelDistribution: r = random (pd, rows, cols, ...)
prob.KernelDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, random returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.KernelDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 189
prob.KernelDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.KernelDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 290
prob.KernelDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower, and upper limit, upper.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.KernelDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 169
prob.KernelDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
prob.LogisticDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1344
statistics: prob.LogisticDistribution
Logistic probability distribution object.

A prob.LogisticDistribution object consists of parameters, a model
description, and sample data for a logistic probability distribution.

The logistic distribution is a continuous probability distribution, which
is commonly used in logistic regression and feedforward neural networks.
It is defined by location parameter mu and scale parameter
sigma.

There are several ways to create a prob.LogisticDistribution
object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.LogisticDistribution (mu,
sigma) to create a logistic distribution with fixed parameter values
mu and sigma.
Use the static method prob.LogisticDistribution.fit (x,
alpha, censor, freq, options) to fit a
distribution to the data in x using the same input arguments as the
logifit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the logistic distribution can be found at
https://en.wikipedia.org/wiki/Logistic_distribution

See also:
fitdist,
makedist,
logicdf,
logiinv,
logipdf,
logirnd,
logifit,
logilike,
logistat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
Logistic probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.LogisticDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 190
prob.LogisticDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.LogisticDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 737
prob.LogisticDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.LogisticDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 210
prob.LogisticDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.LogisticDistribution.LogisticDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 381
prob.LogisticDistribution: pd = LogisticDistribution (mu, sigma)
prob.LogisticDistribution: pd = LogisticDistribution ()
Create a prob.LogisticDistribution object.

mu and sigma are the distribution parameters, which the class
help describes. Called with no arguments the parameters take their
defaults, mu 0 and sigma 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
Create a prob.LogisticDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.LogisticDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 203
prob.LogisticDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.LogisticDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 616
prob.LogisticDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 2x2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then all elements of the variance-covariance are zero. This
property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.LogisticDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 227
prob.LogisticDistribution: property ParameterDescription
Description of parameters

A 2x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.LogisticDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 283
prob.LogisticDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.LogisticDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 204
prob.LogisticDistribution: property ParameterNames
Names of parameters

A 2x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.LogisticDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 284
prob.LogisticDistribution: property ParameterValues
Distribution parameter values

A 2x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the mu and sigma
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.LogisticDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 347
prob.LogisticDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.LogisticDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 386
prob.LogisticDistribution: p = cdf (pd, x)
prob.LogisticDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.LogisticDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 243
prob.LogisticDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.LogisticDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 193
prob.LogisticDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.LogisticDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 165
prob.LogisticDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.LogisticDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 173
prob.LogisticDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.LogisticDistribution.mu


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 189
prob.LogisticDistribution: property mu
Location parameter

A scalar value characterizing the location of the
logistic distribution. You can access the mu
property using dot name assignment.


# name: <cell-element>
# type: sq_string
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Location parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.LogisticDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 219
prob.LogisticDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.LogisticDistribution.paramci


# name: <cell-element>
# type: sq_string
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# length: 977
prob.LogisticDistribution: ci = paramci (pd)
prob.LogisticDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the
confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.LogisticDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 203
prob.LogisticDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.LogisticDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1522
prob.LogisticDistribution: plot (pd)
prob.LogisticDistribution: plot (pd, Name, Value)
prob.LogisticDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.LogisticDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2046
prob.LogisticDistribution: [nlogL, param] = proflik (pd, pnum)
prob.LogisticDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.LogisticDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.LogisticDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.LogisticDistribution: [nlogL, param] = proflik (pd)
prob.LogisticDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the logistic distribution, pnum = 1 selects
the parameter mu and pnum = 2 selects the
parameter sigma.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
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Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.LogisticDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 691
prob.LogisticDistribution: r = random (pd)
prob.LogisticDistribution: r = random (pd, rows)
prob.LogisticDistribution: r = random (pd, rows, cols, ...)
prob.LogisticDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, bisarnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
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# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.LogisticDistribution.sigma


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 198
prob.LogisticDistribution: property sigma
Scale parameter

A positive scalar value characterizing the scale of the
logistic distribution. You can access the sigma
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.LogisticDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 191
prob.LogisticDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.LogisticDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 534
prob.LogisticDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower,
and upper limit, upper. If pd is fitted to data with
fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.LogisticDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 171
prob.LogisticDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.LoglogisticDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1389
statistics: prob.LoglogisticDistribution
Log-logistic probability distribution object.

A prob.LoglogisticDistribution object consists of parameters, a
model description, and sample data for a log-logistic probability
distribution.

The log-logistic distribution is a continuous probability distribution that
models non-negative random variables whose logarithm follows the logistic
distribution. It is defined by location parameter mu and scale
parameter sigma.

There are several ways to create a prob.LoglogisticDistribution
object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.LoglogisticDistribution (mu,
sigma) to create a log-logistic distribution with fixed parameter
values mu and sigma.
Use the static method prob.LoglogisticDistribution.fit
(x, censor, freq, options) to fit a distribution
to the data in x using the same input arguments as the loglfit
function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the log-logistic distribution can be found at
https://en.wikipedia.org/wiki/Log-logistic_distribution

See also:
fitdist,
makedist,
loglcdf,
loglinv,
loglpdf,
loglrnd,
loglfit,
logllike,
loglstat


# name: <cell-element>
# type: sq_string
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# length: 45
Log-logistic probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.LoglogisticDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 193
prob.LoglogisticDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.LoglogisticDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 740
prob.LoglogisticDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.LoglogisticDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 213
prob.LoglogisticDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
prob.LoglogisticDistribution.LoglogisticDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 396
prob.LoglogisticDistribution: pd = LoglogisticDistribution (mu, sigma)
prob.LoglogisticDistribution: pd = LoglogisticDistribution ()
Create a prob.LoglogisticDistribution object.

mu and sigma are the distribution parameters, which the class
help describes. Called with no arguments the parameters take their
defaults, mu 0 and sigma 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
Create a prob.LoglogisticDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.LoglogisticDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 206
prob.LoglogisticDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.LoglogisticDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 619
prob.LoglogisticDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 2x2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


# name: <cell-element>
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# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.LoglogisticDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 230
prob.LoglogisticDistribution: property ParameterDescription
Description of parameters

A 2x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.LoglogisticDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 286
prob.LoglogisticDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.LoglogisticDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 207
prob.LoglogisticDistribution: property ParameterNames
Names of parameters

A 2x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.LoglogisticDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 287
prob.LoglogisticDistribution: property ParameterValues
Distribution parameter values

A 2x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the mu and sigma
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.LoglogisticDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 350
prob.LoglogisticDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.LoglogisticDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 392
prob.LoglogisticDistribution: p = cdf (pd, x)
prob.LoglogisticDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.LoglogisticDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 246
prob.LoglogisticDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.LoglogisticDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 196
prob.LoglogisticDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.LoglogisticDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 168
prob.LoglogisticDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.LoglogisticDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 176
prob.LoglogisticDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.LoglogisticDistribution.mu


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 226
prob.LoglogisticDistribution: property mu
Mean of logarithmic values

A scalar value characterizing the mean of the logarithmic values of the
log-logistic distribution. You can access the mu
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
Mean of logarithmic values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.LoglogisticDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 222
prob.LoglogisticDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.LoglogisticDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 983
prob.LoglogisticDistribution: ci = paramci (pd)
prob.LoglogisticDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.LoglogisticDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 206
prob.LoglogisticDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.LoglogisticDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1531
prob.LoglogisticDistribution: plot (pd)
prob.LoglogisticDistribution: plot (pd, Name, Value)
prob.LoglogisticDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.LoglogisticDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2068
prob.LoglogisticDistribution: [nlogL, param] = proflik (pd, pnum)
prob.LoglogisticDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.LoglogisticDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.LoglogisticDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.LoglogisticDistribution: [nlogL, param] = proflik (pd)
prob.LoglogisticDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the Log-logistic distribution, pnum = 1 selects
the parameter mu and pnum = 2 selects the
parameter sigma.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.LoglogisticDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 702
prob.LoglogisticDistribution: r = random (pd)
prob.LoglogisticDistribution: r = random (pd, rows)
prob.LoglogisticDistribution: r = random (pd, rows, cols, ...)
prob.LoglogisticDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, random returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.LoglogisticDistribution.sigma


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 243
prob.LoglogisticDistribution: property sigma
Scale of logarithmic values

A positive scalar value characterizing the scale of the logarithmic
values of the log-logistic distribution. You can access the sigma
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
Scale of logarithmic values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.LoglogisticDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 194
prob.LoglogisticDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.LoglogisticDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 537
prob.LoglogisticDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower, and upper limit, upper. If pd is fitted to data
with fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.LoglogisticDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 174
prob.LoglogisticDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.LognormalDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1345
statistics: prob.LognormalDistribution
Lognormal probability distribution object.

A prob.LognormalDistribution object consists of parameters, a model
description, and sample data for a lognormal probability distribution.

The lognormal distribution is a continuous probability distribution whose
logarithm is normally distributed. It is defined by mean parameter
mu and standard deviation parameter sigma of the logarithmic
values.

There are several ways to create a prob.LognormalDistribution
object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.LognormalDistribution (mu,
sigma) to create a lognormal distribution with fixed parameter
values mu and sigma.
Use the static method prob.LognormalDistribution.fit (x,
censor, freq, options) to fit a distribution to the
data in x using the same input arguments as the lognfit
function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the lognormal distribution can be found at
https://en.wikipedia.org/wiki/Log-normal_distribution

See also:
fitdist,
makedist,
logncdf,
logninv,
lognpdf,
lognrnd,
lognfit,
lognlike,
lognstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
Lognormal probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.LognormalDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 191
prob.LognormalDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.LognormalDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 738
prob.LognormalDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.LognormalDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 211
prob.LognormalDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.LognormalDistribution.LognormalDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 386
prob.LognormalDistribution: pd = LognormalDistribution (mu, sigma)
prob.LognormalDistribution: pd = LognormalDistribution ()
Create a prob.LognormalDistribution object.

mu and sigma are the distribution parameters, which the class
help describes. Called with no arguments the parameters take their
defaults, mu 0 and sigma 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Create a prob.LognormalDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.LognormalDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 204
prob.LognormalDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.LognormalDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 617
prob.LognormalDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 2x2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
prob.LognormalDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 228
prob.LognormalDistribution: property ParameterDescription
Description of parameters

A 2x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.LognormalDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 284
prob.LognormalDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.LognormalDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 205
prob.LognormalDistribution: property ParameterNames
Names of parameters

A 2x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.LognormalDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 285
prob.LognormalDistribution: property ParameterValues
Distribution parameter values

A 2x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the mu and sigma
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.LognormalDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 348
prob.LognormalDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.LognormalDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 388
prob.LognormalDistribution: p = cdf (pd, x)
prob.LognormalDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.LognormalDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 244
prob.LognormalDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.LognormalDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 194
prob.LognormalDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.LognormalDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 166
prob.LognormalDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.LognormalDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 174
prob.LognormalDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.LognormalDistribution.mu


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 221
prob.LognormalDistribution: property mu
Mean of logarithmic values

A scalar value characterizing the mean of the logarithmic values of the
lognormal distribution. You can access the mu
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
Mean of logarithmic values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.LognormalDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 220
prob.LognormalDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.LognormalDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 979
prob.LognormalDistribution: ci = paramci (pd)
prob.LognormalDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.LognormalDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 204
prob.LognormalDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.LognormalDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1525
prob.LognormalDistribution: plot (pd)
prob.LognormalDistribution: plot (pd, Name, Value)
prob.LognormalDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.LognormalDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2053
prob.LognormalDistribution: [nlogL, param] = proflik (pd, pnum)
prob.LognormalDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.LognormalDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.LognormalDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.LognormalDistribution: [nlogL, param] = proflik (pd)
prob.LognormalDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the Lognormal distribution, pnum = 1 selects
the parameter mu and pnum = 2 selects the
parameter sigma.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.LognormalDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 695
prob.LognormalDistribution: r = random (pd)
prob.LognormalDistribution: r = random (pd, rows)
prob.LognormalDistribution: r = random (pd, rows, cols, ...)
prob.LognormalDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, lognrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.LognormalDistribution.sigma


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 264
prob.LognormalDistribution: property sigma
Standard deviation of logarithmic values

A positive scalar value characterizing the standard deviation of the
logarithmic values of the lognormal distribution. You can access the
sigma property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
Standard deviation of logarithmic values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.LognormalDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 192
prob.LognormalDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.LognormalDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 535
prob.LognormalDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower, and upper limit, upper. If pd is fitted to data
with fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.LognormalDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 172
prob.LognormalDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.LoguniformDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 939
statistics: prob.LoguniformDistribution
Log-uniform probability distribution object.

A prob.LoguniformDistribution object consists of parameters and a
model description for a log-uniform probability distribution.

The log-uniform distribution is a continuous probability distribution that
is constant between locations Lower and Upper on a logarithmic
scale.

There are several ways to create a prob.LoguniformDistribution
object.

Create a distribution with specified parameter values using the
makedist function.
Use the constructor prob.LoguniformDistribution (Lower,
Upper) to create a log-uniform distribution with specified parameter
values Lower and Upper.

It is highly recommended to use makedist function to create
probability distribution objects, instead of the class constructor.

Further information about the log-uniform distribution can be found at
https://en.wikipedia.org/wiki/Reciprocal_distribution

See also:
makedist


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Log-uniform probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.LoguniformDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 192
prob.LoguniformDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.LoguniformDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 212
prob.LoguniformDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.LoguniformDistribution.LoguniformDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 400
prob.LoguniformDistribution: pd = LoguniformDistribution (Lower, Upper)
prob.LoguniformDistribution: pd = LoguniformDistribution ()
Create a prob.LoguniformDistribution object.

Lower and Upper are the distribution parameters, which the
class help describes. Called with no arguments the parameters take their
defaults, Lower 1 and Upper 4.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Create a prob.LoguniformDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.LoguniformDistribution.Lower


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 205
prob.LoguniformDistribution: property Lower
Lower limit

A positive scalar value characterizing the lower limit of the
log-uniform distribution. You can access the Lower
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
Lower limit



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.LoguniformDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 205
prob.LoguniformDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.LoguniformDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 229
prob.LoguniformDistribution: property ParameterDescription
Description of parameters

A 2x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.LoguniformDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 206
prob.LoguniformDistribution: property ParameterNames
Names of parameters

A 2x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.LoguniformDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 289
prob.LoguniformDistribution: property ParameterValues
Distribution parameter values

A 2x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the Lower and Upper
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.LoguniformDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 349
prob.LoguniformDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.LoguniformDistribution.Upper


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 205
prob.LoguniformDistribution: property Upper
Upper limit

A positive scalar value characterizing the upper limit of the
log-uniform distribution. You can access the Upper
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
Upper limit



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.LoguniformDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 472
prob.LoguniformDistribution: p = cdf (pd, x)
prob.LoguniformDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.

x must be double or single; integer, logical,
and character arrays are rejected.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.LoguniformDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 327
prob.LoguniformDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.

p must be double or single; integer, logical,
and character arrays are rejected.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.LoguniformDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 195
prob.LoguniformDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.LoguniformDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 167
prob.LoguniformDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.LoguniformDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 175
prob.LoguniformDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.LoguniformDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 287
prob.LoguniformDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.

x must be double or single; integer, logical,
and character arrays are rejected.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.LoguniformDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1101
prob.LoguniformDistribution: plot (pd)
prob.LoguniformDistribution: plot (pd, Name, Value)
prob.LoguniformDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF).
'cdf' plots the cumulative density function (CDF).
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.LoguniformDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 698
prob.LoguniformDistribution: r = random (pd)
prob.LoguniformDistribution: r = random (pd, rows)
prob.LoguniformDistribution: r = random (pd, rows, cols, ...)
prob.LoguniformDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, random returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.LoguniformDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 193
prob.LoguniformDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.LoguniformDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 294
prob.LoguniformDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower, and upper limit, upper.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.LoguniformDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 173
prob.LoguniformDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.MultinomialDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1080
statistics: prob.MultinomialDistribution
Multinomial probability distribution object.

A prob.MultinomialDistribution object consists of parameters, a
model description, and sample data for a multinomial probability
distribution.

The multinomial distribution is a discrete probability distribution that
models the outcomes of n independent trials of a k-category system, where
each trial has a probability of falling into each category. It is
defined by the vector of probabilities for each outcome.

There are several ways to create a prob.MultinomialDistribution
object.

Create a distribution with specified parameter values using the
makedist function.
Use the constructor
prob.MultinomialDistribution
(Probabilities)
to create a multinomial distribution with specified parameter values.

It is highly recommended to use the makedist function to create
probability distribution objects, instead of the constructor.

Further information about the multinomial distribution can be found at
https://en.wikipedia.org/wiki/Multinomial_distribution

See also:
makedist,
mnpdf,
mnrnd


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Multinomial probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.MultinomialDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 193
prob.MultinomialDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.MultinomialDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 213
prob.MultinomialDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
prob.MultinomialDistribution.MultinomialDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 404
prob.MultinomialDistribution: pd = MultinomialDistribution (Probabilities)
prob.MultinomialDistribution: pd = MultinomialDistribution ()
Create a prob.MultinomialDistribution object.

Probabilities is the distribution parameter, which the class help
describes. Called with no arguments the parameter takes its default,
Probabilities [0.5, 0.5].

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
Create a prob.MultinomialDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.MultinomialDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 206
prob.MultinomialDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.MultinomialDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 230
prob.MultinomialDistribution: property ParameterDescription
Description of parameters

A 1x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.MultinomialDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 207
prob.MultinomialDistribution: property ParameterNames
Names of parameters

A 1x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.MultinomialDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 282
prob.MultinomialDistribution: property ParameterValues
Distribution parameter values

A numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the Probabilities
property.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.MultinomialDistribution.Probabilities


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 192
prob.MultinomialDistribution: property Probabilities
Outcome probabilities

A row vector of probabilities for each outcome. You can access the
Probabilities property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 21
Outcome probabilities



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.MultinomialDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 350
prob.MultinomialDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.MultinomialDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 558
prob.MultinomialDistribution: p = cdf (pd, x)
prob.MultinomialDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.

x must be double, single, or an integer type;
logical and character arrays are rejected. Integer input is promoted
to double, so the result is always a probability.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.MultinomialDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 328
prob.MultinomialDistribution: p = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

p = icdf (pd, x) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in x.

p must be double or single; integer, logical, and
character arrays are rejected.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.MultinomialDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 196
prob.MultinomialDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.MultinomialDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 168
prob.MultinomialDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.MultinomialDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 176
prob.MultinomialDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.MultinomialDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 372
prob.MultinomialDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.

x must be double, single, or an integer type;
logical and character arrays are rejected. Integer input is promoted
to double, so the result is always a probability.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.MultinomialDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1530
prob.MultinomialDistribution: plot (pd)
prob.MultinomialDistribution: plot (pd, Name, Value)
prob.MultinomialDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.MultinomialDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 701
prob.MultinomialDistribution: y = random (pd)
prob.MultinomialDistribution: y = random (pd, rows)
prob.MultinomialDistribution: y = random (pd, rows, cols, ...)
prob.MultinomialDistribution: y = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, mnrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.MultinomialDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 194
prob.MultinomialDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.MultinomialDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 523
prob.MultinomialDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd) returns a probability distribution
t, which is the probability distribution pd truncated to the
specified interval with lower limit, lower, and upper limit,
upper. If pd is fitted to data with fitdist, the
returned probability distribution t is not fitted, does not contain
any data or estimated values, and it is as it has been created with the
makedist function, but it includes the truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.MultinomialDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 184
prob.MultinomialDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the standard deviation of the
probability distribution object, pd.


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Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
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prob.NakagamiDistribution


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statistics: prob.NakagamiDistribution
Nakagami probability distribution object.

A prob.NakagamiDistribution object consists of parameters, a model
description, and sample data for a Nakagami probability distribution.

The Nakagami distribution is a continuous probability distribution that
models the amplitude of received signals after maximum ratio diversity
combining. It is defined by shape parameter mu and spread parameter
omega.

There are several ways to create a prob.NakagamiDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.NakagamiDistribution (mu,
omega) to create a Nakagami distribution with fixed parameter
values mu and omega.
Use the static method prob.NakagamiDistribution.fit (x,
censor, freq, options) to fit a distribution to the data
in x using the same input arguments as the nakafit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the Nakagami distribution can be found at
https://en.wikipedia.org/wiki/Nakagami_distribution

See also:
fitdist,
makedist,
nakacdf,
nakainv,
nakapdf,
nakarnd,
nakafit,
nakalike,
nakastat


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Nakagami probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.NakagamiDistribution.DistributionName


# name: <cell-element>
# type: sq_string
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# length: 190
prob.NakagamiDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.NakagamiDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 737
prob.NakagamiDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
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Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.NakagamiDistribution.IsTruncated


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# type: sq_string
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# length: 210
prob.NakagamiDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
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# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.NakagamiDistribution.NakagamiDistribution


# name: <cell-element>
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# length: 381
prob.NakagamiDistribution: pd = NakagamiDistribution (mu, omega)
prob.NakagamiDistribution: pd = NakagamiDistribution ()
Create a prob.NakagamiDistribution object.

mu and omega are the distribution parameters, which the class
help describes. Called with no arguments the parameters take their
defaults, mu 1 and omega 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
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Create a prob.NakagamiDistribution object.



# name: <cell-element>
# type: sq_string
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# length: 39
prob.NakagamiDistribution.NumParameters


# name: <cell-element>
# type: sq_string
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# length: 203
prob.NakagamiDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.NakagamiDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 616
prob.NakagamiDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 2x2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


# name: <cell-element>
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# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.NakagamiDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 227
prob.NakagamiDistribution: property ParameterDescription
Description of parameters

A 2x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.NakagamiDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 283
prob.NakagamiDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.NakagamiDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 204
prob.NakagamiDistribution: property ParameterNames
Names of parameters

A 2x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.NakagamiDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 284
prob.NakagamiDistribution: property ParameterValues
Distribution parameter values

A 2x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the mu and omega
properties.


# name: <cell-element>
# type: sq_string
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# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.NakagamiDistribution.Truncation


# name: <cell-element>
# type: sq_string
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# length: 347
prob.NakagamiDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
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# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.NakagamiDistribution.cdf


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# type: sq_string
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# length: 386
prob.NakagamiDistribution: p = cdf (pd, x)
prob.NakagamiDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


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Compute the cumulative distribution function (CDF).



# name: <cell-element>
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# length: 30
prob.NakagamiDistribution.icdf


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# type: sq_string
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# length: 243
prob.NakagamiDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


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Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
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# length: 29
prob.NakagamiDistribution.iqr


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prob.NakagamiDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


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# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.NakagamiDistribution.mean


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# type: sq_string
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# length: 165
prob.NakagamiDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


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Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.NakagamiDistribution.median


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# type: sq_string
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# length: 173
prob.NakagamiDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
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# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.NakagamiDistribution.mu


# name: <cell-element>
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# length: 192
prob.NakagamiDistribution: property mu
Shape parameter

A positive scalar value characterizing the shape of the
Nakagami distribution. You can access the mu
property using dot name assignment.


# name: <cell-element>
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Shape parameter



# name: <cell-element>
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# length: 35
prob.NakagamiDistribution.negloglik


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# length: 219
prob.NakagamiDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


# name: <cell-element>
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# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.NakagamiDistribution.omega


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# type: sq_string
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# length: 200
prob.NakagamiDistribution: property omega
Spread parameter

A positive scalar value characterizing the spread of the
Nakagami distribution. You can access the omega
property using dot name assignment.


# name: <cell-element>
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# length: 16
Spread parameter



# name: <cell-element>
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# elements: 1
# length: 33
prob.NakagamiDistribution.paramci


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# length: 977
prob.NakagamiDistribution: ci = paramci (pd)
prob.NakagamiDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


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Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.NakagamiDistribution.pdf


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# type: sq_string
# elements: 1
# length: 203
prob.NakagamiDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


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Compute the probability distribution function (PDF).



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# type: sq_string
# elements: 1
# length: 30
prob.NakagamiDistribution.plot


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# length: 1522
prob.NakagamiDistribution: plot (pd)
prob.NakagamiDistribution: plot (pd, Name, Value)
prob.NakagamiDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
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# length: 39
Plot a probability distribution object.



# name: <cell-element>
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# length: 33
prob.NakagamiDistribution.proflik


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# type: sq_string
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# length: 2046
prob.NakagamiDistribution: [nlogL, param] = proflik (pd, pnum)
prob.NakagamiDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.NakagamiDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.NakagamiDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.NakagamiDistribution: [nlogL, param] = proflik (pd)
prob.NakagamiDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the Nakagami distribution, pnum = 1 selects
the parameter mu and pnum = 2 selects the
parameter omega.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


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Profile likelihood function for a probability distribution object.



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# length: 32
prob.NakagamiDistribution.random


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# type: sq_string
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# length: 691
prob.NakagamiDistribution: r = random (pd)
prob.NakagamiDistribution: r = random (pd, rows)
prob.NakagamiDistribution: r = random (pd, rows, cols, ...)
prob.NakagamiDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, betarnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
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# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
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# length: 29
prob.NakagamiDistribution.std


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# type: sq_string
# elements: 1
# length: 191
prob.NakagamiDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


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# type: sq_string
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# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.NakagamiDistribution.truncate


# name: <cell-element>
# type: sq_string
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# length: 534
prob.NakagamiDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower, and upper limit, upper. If pd is fitted to data
with fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
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Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.NakagamiDistribution.var


# name: <cell-element>
# type: sq_string
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# length: 171
prob.NakagamiDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.NegativeBinomialDistribution


# name: <cell-element>
# type: sq_string
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# length: 1511
statistics: prob.NegativeBinomialDistribution
Negative binomial probability distribution object.

A prob.NegativeBinomialDistribution object consists of parameters, a
model description, and sample data for a negative binomial probability
distribution.

The negative binomial distribution is a discrete probability distribution
that models the number of failures in a sequence of independent and
identically distributed Bernoulli trials before a specified (non-random)
number of successes occurs. It is defined by the number of successes
R and the probability of success P.

There are several ways to create a prob.NegativeBinomialDistribution
object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor
prob.NegativeBinomialDistribution (R, P) to create a
negative binomial distribution with fixed parameter values R and
P.
Use the static method
prob.NegativeBinomialDistribution.fit
(x,
freq, options) to fit a distribution to the data in x
using the same input arguments as the nbinfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the negative binomial distribution can be found
at https://en.wikipedia.org/wiki/Negative_binomial_distribution

See also:
fitdist,
makedist,
nbincdf,
nbininv,
nbinpdf,
nbinrnd,
nbinfit,
nbinlike,
nbinstat


# name: <cell-element>
# type: sq_string
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# length: 50
Negative binomial probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.NegativeBinomialDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 198
prob.NegativeBinomialDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.NegativeBinomialDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 745
prob.NegativeBinomialDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
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Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.NegativeBinomialDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
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# length: 218
prob.NegativeBinomialDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
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# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
prob.NegativeBinomialDistribution.NegativeBinomialDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 408
prob.NegativeBinomialDistribution: pd = NegativeBinomialDistribution (R, P)
prob.NegativeBinomialDistribution: pd = NegativeBinomialDistribution ()
Create a prob.NegativeBinomialDistribution object.

R and P are the distribution parameters, which the class help
describes. Called with no arguments the parameters take their defaults,
R 1 and P 0.5.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
Create a prob.NegativeBinomialDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
prob.NegativeBinomialDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 211
prob.NegativeBinomialDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.NegativeBinomialDistribution.P


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 222
prob.NegativeBinomialDistribution: property P
Probability of success

A scalar value characterizing the probability of success in the
negative binomial distribution. You can access the P
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 22
Probability of success



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 53
prob.NegativeBinomialDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 624
prob.NegativeBinomialDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 2x2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 54
prob.NegativeBinomialDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 235
prob.NegativeBinomialDistribution: property ParameterDescription
Description of parameters

A 2x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.NegativeBinomialDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 291
prob.NegativeBinomialDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.NegativeBinomialDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 212
prob.NegativeBinomialDistribution: property ParameterNames
Names of parameters

A 2x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.NegativeBinomialDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 287
prob.NegativeBinomialDistribution: property ParameterValues
Distribution parameter values

A 2x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the R and P
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.NegativeBinomialDistribution.R


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 216
prob.NegativeBinomialDistribution: property R
Number of successes

A scalar value characterizing the number of successes in the
negative binomial distribution. You can access the R
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Number of successes



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.NegativeBinomialDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 355
prob.NegativeBinomialDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.NegativeBinomialDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 402
prob.NegativeBinomialDistribution: p = cdf (pd, x)
prob.NegativeBinomialDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.NegativeBinomialDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 251
prob.NegativeBinomialDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.NegativeBinomialDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 201
prob.NegativeBinomialDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.NegativeBinomialDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 173
prob.NegativeBinomialDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.NegativeBinomialDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 181
prob.NegativeBinomialDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.NegativeBinomialDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 227
prob.NegativeBinomialDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.NegativeBinomialDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 993
prob.NegativeBinomialDistribution: ci = paramci (pd)
prob.NegativeBinomialDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.NegativeBinomialDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 211
prob.NegativeBinomialDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.NegativeBinomialDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1546
prob.NegativeBinomialDistribution: plot (pd)
prob.NegativeBinomialDistribution: plot (pd, Name, Value)
prob.NegativeBinomialDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.NegativeBinomialDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2098
prob.NegativeBinomialDistribution: [nlogL, param] = proflik (pd, pnum)
prob.NegativeBinomialDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.NegativeBinomialDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.NegativeBinomialDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.NegativeBinomialDistribution: [nlogL, param] = proflik (pd)
prob.NegativeBinomialDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the negative binomial distribution, pnum = 1 selects
the parameter R and pnum = 2 selects the
parameter P.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.NegativeBinomialDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 724
prob.NegativeBinomialDistribution: r = random (pd)
prob.NegativeBinomialDistribution: r = random (pd, rows)
prob.NegativeBinomialDistribution: r = random (pd, rows, cols, ...)
prob.NegativeBinomialDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, nbindrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.NegativeBinomialDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 199
prob.NegativeBinomialDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.NegativeBinomialDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 542
prob.NegativeBinomialDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower, and upper limit, upper. If pd is fitted to data
with fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.NegativeBinomialDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 179
prob.NegativeBinomialDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 23
prob.NormalDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1304
statistics: prob.NormalDistribution
Normal probability distribution object.

A prob.NormalDistribution object consists of parameters, a model
description, and sample data for a normal probability distribution.

The normal distribution is a continuous probability distribution that is
symmetric about the mean, mu, showing that data near the mean are
more frequent in occurrence than data far from the mean. It is defined by
location parameter mu and scale parameter sigma.

There are several ways to create a prob.NormalDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor
prob.NormalDistribution (mu,
sigma)
to create a normal distribution with fixed parameter values mu and
sigma.
Use the static method prob.NormalDistribution.fit (x,
censor, freq, options) to fit a distribution to data
x.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the normal distribution can be found at
https://en.wikipedia.org/wiki/Normal_distribution

See also:
fitdist,
makedist,
normcdf,
norminv,
normpdf,
normrnd,
normfit,
normlike,
normstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Normal probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.NormalDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 188
prob.NormalDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.NormalDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 735
prob.NormalDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.NormalDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 208
prob.NormalDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.NormalDistribution.NormalDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 371
prob.NormalDistribution: pd = NormalDistribution (mu, sigma)
prob.NormalDistribution: pd = NormalDistribution ()
Create a prob.NormalDistribution object.

mu and sigma are the distribution parameters, which the class
help describes. Called with no arguments the parameters take their
defaults, mu 0 and sigma 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
Create a prob.NormalDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.NormalDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 201
prob.NormalDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.NormalDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 614
prob.NormalDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 2x2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only meaningful
when the distribution was fitted to data. If the distribution object was
created with fixed parameters, or a parameter of a fitted distribution is
modified, then all elements of the variance-covariance are zero. This
property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.NormalDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 225
prob.NormalDistribution: property ParameterDescription
Description of parameters

A 2x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.NormalDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 281
prob.NormalDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.NormalDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 202
prob.NormalDistribution: property ParameterNames
Names of parameters

A 2x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.NormalDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 282
prob.NormalDistribution: property ParameterValues
Distribution parameter values

A 2x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the mu and sigma
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.NormalDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 345
prob.NormalDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.NormalDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 382
prob.NormalDistribution: p = cdf (pd, x)
prob.NormalDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.NormalDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 241
prob.NormalDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.NormalDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 191
prob.NormalDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.NormalDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 163
prob.NormalDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.NormalDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 171
prob.NormalDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.NormalDistribution.mu


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 185
prob.NormalDistribution: property mu
Location parameter

A scalar value characterizing the location of the normal distribution.
You can access the mu property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
Location parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.NormalDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 217
prob.NormalDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.NormalDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 973
prob.NormalDistribution: ci = paramci (pd)
prob.NormalDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.NormalDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 201
prob.NormalDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.NormalDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1516
prob.NormalDistribution: plot (pd)
prob.NormalDistribution: plot (pd, Name, Value)
prob.NormalDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.NormalDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2032
prob.NormalDistribution: [nlogL, param] = proflik (pd, pnum)
prob.NormalDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.NormalDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.NormalDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.NormalDistribution: [nlogL, param] = proflik (pd)
prob.NormalDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the normal distribution, pnum = 1 selects the
parameter mu and pnum = 2 selects the parameter
sigma.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.NormalDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 683
prob.NormalDistribution: r = random (pd)
prob.NormalDistribution: r = random (pd, rows)
prob.NormalDistribution: r = random (pd, rows, cols, ...)
prob.NormalDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, normrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.NormalDistribution.sigma


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 194
prob.NormalDistribution: property sigma
Scale parameter

A positive scalar value characterizing the scale of the normal
distribution. You can access the sigma property using dot name
assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.NormalDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 189
prob.NormalDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.NormalDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 532
prob.NormalDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower, and upper limit, upper. If pd is fitted to data
with fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.NormalDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 169
prob.NormalDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.PiecewiseLinearDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1178
statistics: prob.PiecewiseLinearDistribution
Piecewise linear probability distribution object.

A prob.PiecewiseLinearDistribution object consists of parameters, a
model description, and sample data for a piecewise linear probability
distribution.

The piecewise linear distribution is a continuous probability distribution
that is defined by a set of points where the cumulative distribution
function (CDF) changes slope. It is defined by a vector of x values
and a corresponding vector of CDF values Fx.

There are several ways to create a prob.PiecewiseLinearDistribution
object.

Create a distribution with specified parameter values using the
makedist function.
Use the constructor prob.PiecewiseLinearDistribution (x,
Fx) to create a piecewise linear distribution with specified
parameter values x and Fx.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the piecewise linear distribution can be found at
https://en.wikipedia.org/wiki/Piecewise_linear_function

See also:
makedist,
plcdf,
plinv,
plpdf,
plrnd,
plstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Piecewise linear probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
prob.PiecewiseLinearDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 197
prob.PiecewiseLinearDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.PiecewiseLinearDistribution.Fx


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 242
prob.PiecewiseLinearDistribution: property Fx
Vector of CDF values

A numeric row vector of CDF values that correspond to each value in
x, reported as a row whichever way it was given. You can access
the Fx property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Vector of CDF values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.PiecewiseLinearDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 217
prob.PiecewiseLinearDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.PiecewiseLinearDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 210
prob.PiecewiseLinearDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 53
prob.PiecewiseLinearDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 234
prob.PiecewiseLinearDistribution: property ParameterDescription
Description of parameters

A 2x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
prob.PiecewiseLinearDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 211
prob.PiecewiseLinearDistribution: property ParameterNames
Names of parameters

A 2x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.PiecewiseLinearDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 287
prob.PiecewiseLinearDistribution: property ParameterValues
Distribution parameter values

A 2x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the x and Fx
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
prob.PiecewiseLinearDistribution.PiecewiseLinearDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 414
prob.PiecewiseLinearDistribution: pd = PiecewiseLinearDistribution (x, Fx)
prob.PiecewiseLinearDistribution: pd = PiecewiseLinearDistribution ()
Create a prob.PiecewiseLinearDistribution object.

x and Fx are the distribution parameters, which the class
help describes. Called with no arguments the parameters take their
defaults, x [0; 1] and Fx [0; 1].

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Create a prob.PiecewiseLinearDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.PiecewiseLinearDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 354
prob.PiecewiseLinearDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.PiecewiseLinearDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 400
prob.PiecewiseLinearDistribution: p = cdf (pd, x)
prob.PiecewiseLinearDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.PiecewiseLinearDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 250
prob.PiecewiseLinearDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.PiecewiseLinearDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 200
prob.PiecewiseLinearDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.PiecewiseLinearDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 172
prob.PiecewiseLinearDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.PiecewiseLinearDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 180
prob.PiecewiseLinearDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.PiecewiseLinearDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 210
prob.PiecewiseLinearDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.PiecewiseLinearDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1543
prob.PiecewiseLinearDistribution: plot (pd)
prob.PiecewiseLinearDistribution: plot (pd, Name, Value)
prob.PiecewiseLinearDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.PiecewiseLinearDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 719
prob.PiecewiseLinearDistribution: r = random (pd)
prob.PiecewiseLinearDistribution: r = random (pd, rows)
prob.PiecewiseLinearDistribution: r = random (pd, rows, cols, ...)
prob.PiecewiseLinearDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, betarnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.PiecewiseLinearDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 198
prob.PiecewiseLinearDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.PiecewiseLinearDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 527
prob.PiecewiseLinearDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd) returns a probability distribution
t, which is the probability distribution pd truncated to the
specified interval with lower limit, lower, and upper limit,
upper. If pd is fitted to data with fitdist, the
returned probability distribution t is not fitted, does not contain
any data or estimated values, and it is as it has been created with the
makedist function, but it includes the truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.PiecewiseLinearDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 188
prob.PiecewiseLinearDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.PiecewiseLinearDistribution.x


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 232
prob.PiecewiseLinearDistribution: property x
Vector of x values

A numeric row vector of x values at which the CDF changes slope,
reported as a row whichever way it was given. You can access the
x property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
Vector of x values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 24
prob.PoissonDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1328
statistics: prob.PoissonDistribution
Poisson probability distribution object.

A prob.PoissonDistribution object consists of parameters, a model
description, and sample data for a Poisson probability distribution.

The Poisson distribution is a discrete probability distribution that
models the number of events occurring in a fixed interval of time or space,
given a constant average rate of occurrence. It is defined by the rate
parameter lambda.

There are several ways to create a prob.PoissonDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.PoissonDistribution (lambda)
to create a Poisson distribution with fixed parameter value lambda.
Use the static method prob.PoissonDistribution.fit (x,
freq) to fit a distribution to the data in x using
the same input arguments as the poissfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the Poisson distribution can be found at
https://en.wikipedia.org/wiki/Poisson_distribution

See also:
fitdist,
makedist,
poisscdf,
poissinv,
poisspdf,
poissrnd,
poissfit,
poisslike,
poisstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
Poisson probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.PoissonDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 189
prob.PoissonDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.PoissonDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 736
prob.PoissonDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.PoissonDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 209
prob.PoissonDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.PoissonDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 202
prob.PoissonDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.PoissonDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 415
prob.PoissonDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 1x1 numeric matrix containing the variance of the parameter
estimate. This matrix is only meaningful when the distribution was fitted
to data. If the distribution object was created with fixed parameters,
or a parameter of a fitted distribution is modified, then the
variance is zero. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.PoissonDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 226
prob.PoissonDistribution: property ParameterDescription
Description of parameters

A 1x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.PoissonDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 277
prob.PoissonDistribution: property ParameterIsFixed
Flag for fixed parameters

A logical scalar specifying whether the parameter is fixed or estimated.
A true value corresponds to a fixed parameter, a false
value corresponds to a parameter estimate. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.PoissonDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 203
prob.PoissonDistribution: property ParameterNames
Names of parameters

A 1x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.PoissonDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 275
prob.PoissonDistribution: property ParameterValues
Distribution parameter values

A 1x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the lambda property.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.PoissonDistribution.PoissonDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 354
prob.PoissonDistribution: pd = PoissonDistribution (lambda)
prob.PoissonDistribution: pd = PoissonDistribution ()
Create a prob.PoissonDistribution object.

lambda is the distribution parameter, which the class help
describes. Called with no arguments the parameter takes its default,
lambda 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
Create a prob.PoissonDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.PoissonDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 354
prob.PoissonDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. The first element contains the lower boundary,
the second element contains the upper boundary. This property is
read-only. You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.PoissonDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 384
prob.PoissonDistribution: p = cdf (pd, x)
prob.PoissonDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.PoissonDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 242
prob.PoissonDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.PoissonDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 192
prob.PoissonDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.PoissonDistribution.lambda


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 196
prob.PoissonDistribution: property lambda
Rate parameter

A positive scalar value characterizing the rate of the
Poisson distribution. You can access the lambda
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 14
Rate parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.PoissonDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 164
prob.PoissonDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.PoissonDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 172
prob.PoissonDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.PoissonDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 218
prob.PoissonDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.PoissonDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 975
prob.PoissonDistribution: ci = paramci (pd)
prob.PoissonDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.PoissonDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 202
prob.PoissonDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.PoissonDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1459
prob.PoissonDistribution: plot (pd)
prob.PoissonDistribution: plot (pd, Name, Value)
prob.PoissonDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions.
'Parent' An axes graphics object for the plot.
If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.PoissonDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2002
prob.PoissonDistribution: [nlogL, param] = proflik (pd, pnum)
prob.PoissonDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.PoissonDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.PoissonDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.PoissonDistribution: [nlogL, param] = proflik (pd)
prob.PoissonDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the Poisson distribution, pnum = 1 selects the
parameter lambda.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the user-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.PoissonDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 688
prob.PoissonDistribution: r = random (pd)
prob.PoissonDistribution: r = random (pd, rows)
prob.PoissonDistribution: r = random (pd, rows, cols, ...)
prob.PoissonDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, poissrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.PoissonDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 190
prob.PoissonDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.PoissonDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 533
prob.PoissonDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower, and upper limit, upper. If pd is fitted to data
with fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.PoissonDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 170
prob.PoissonDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.ProbabilityDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 757
statistics: prob.ProbabilityDistribution
Abstract base class of the probability distribution objects.

It holds the behaviour every distribution object shares -- how it is
displayed, how its parameter confidence intervals are computed, how it is
plotted and how a profile likelihood is taken -- as protected methods, so
the 29 distribution classes inherit one implementation and no part of it is
reachable from outside them.

These helpers were ordinary files in a private directory until the
classes moved into the prob namespace. Octave does not resolve a
private directory from inside a package directory, for a classdef or
for a plain function, so the only way to keep them out of the public
interface is to make them protected methods of a shared base.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Abstract base class of the probability distribution objects.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
prob.RayleighDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1512
statistics: prob.RayleighDistribution
Rayleigh probability distribution object.

A prob.RayleighDistribution object consists of parameters, a model
description, and sample data for a Rayleigh probability distribution.

The Rayleigh distribution is a continuous probability distribution for
nonnegative random variables. It is often used to model the magnitude of
a vector in two dimensions where the components are normally distributed
with zero mean and equal variance. It is defined by scale parameter
B.

B is the sigma of the usual mathematical notation. The
rayl* functions name the same quantity sigma; this class
follows MATLAB.

There are several ways to create a prob.RayleighDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.RayleighDistribution (B)
to create a Rayleigh distribution with fixed parameter value B.
Use the static method prob.RayleighDistribution.fit (x,
censor, freq) to fit a distribution to the data in x
using the same input arguments as the raylfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the Rayleigh distribution can be found at
https://en.wikipedia.org/wiki/Rayleigh_distribution

See also:
fitdist,
makedist,
raylcdf,
raylinv,
raylpdf,
raylrnd,
raylfit,
rayllike,
raylstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
Rayleigh probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.RayleighDistribution.B


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 190
prob.RayleighDistribution: property B
Scale parameter

A positive scalar value characterizing the scale of the
Rayleigh distribution. You can access the B
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.RayleighDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 190
prob.RayleighDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.RayleighDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 737
prob.RayleighDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.RayleighDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 210
prob.RayleighDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.RayleighDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 203
prob.RayleighDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.RayleighDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 612
prob.RayleighDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.RayleighDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 223
prob.RayleighDistribution: property ParameterDescription
Description of parameters

A cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.RayleighDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 279
prob.RayleighDistribution: property ParameterIsFixed
Flag for fixed parameters

A logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.RayleighDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 200
prob.RayleighDistribution: property ParameterNames
Names of parameters

A cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.RayleighDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 267
prob.RayleighDistribution: property ParameterValues
Distribution parameter values

A numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the B
property.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.RayleighDistribution.RayleighDistribution


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prob.RayleighDistribution: pd = RayleighDistribution (B)
prob.RayleighDistribution: pd = RayleighDistribution ()
Create a prob.RayleighDistribution object.

B is the distribution parameter, which the class help describes.
Called with no arguments the parameter takes its default, B 1.

makedist is the usual way to create a distribution object.


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Create a prob.RayleighDistribution object.



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prob.RayleighDistribution.Truncation


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prob.RayleighDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


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Truncation interval



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prob.RayleighDistribution.cdf


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prob.RayleighDistribution: p = cdf (pd, x)
prob.RayleighDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


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Compute the cumulative distribution function (CDF).



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prob.RayleighDistribution.icdf


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prob.RayleighDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


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Compute the inverse cumulative distribution function (iCDF).



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prob.RayleighDistribution.iqr


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prob.RayleighDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


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Compute the interquartile range of a probability distribution.



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prob.RayleighDistribution.mean


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prob.RayleighDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


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Compute the mean of a probability distribution.



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prob.RayleighDistribution.median


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prob.RayleighDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


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Compute the median of a probability distribution.



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prob.RayleighDistribution.negloglik


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prob.RayleighDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


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Compute the negative loglikelihood of a probability distribution.



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prob.RayleighDistribution.paramci


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prob.RayleighDistribution: ci = paramci (pd)
prob.RayleighDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


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Compute the confidence intervals for probability distribution parameters.



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prob.RayleighDistribution.pdf


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prob.RayleighDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


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Compute the probability distribution function (PDF).



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prob.RayleighDistribution.plot


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prob.RayleighDistribution: plot (pd)
prob.RayleighDistribution: plot (pd, Name, Value)
prob.RayleighDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


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Plot a probability distribution object.



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prob.RayleighDistribution.proflik


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prob.RayleighDistribution: [nlogL, param] = proflik (pd, pnum)
prob.RayleighDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.RayleighDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.RayleighDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.RayleighDistribution: [nlogL, param] = proflik (pd)
prob.RayleighDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the Rayleigh distribution, pnum = 1 selects
the parameter B.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


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Profile likelihood function for a probability distribution object.



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prob.RayleighDistribution.random


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prob.RayleighDistribution: r = random (pd)
prob.RayleighDistribution: r = random (pd, rows)
prob.RayleighDistribution: r = random (pd, rows, cols, ...)
prob.RayleighDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, betarnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


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Generate random arrays from the probability distribution object.



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prob.RayleighDistribution.std


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prob.RayleighDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


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Compute the standard deviation of a probability distribution.



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prob.RayleighDistribution.truncate


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prob.RayleighDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower, and upper limit, upper. If pd is fitted to data
with fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


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Truncate a probability distribution.



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prob.RayleighDistribution.var


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prob.RayleighDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


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Compute the variance of a probability distribution.



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prob.RicianDistribution


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statistics: prob.RicianDistribution
Rician probability distribution object.

A prob.RicianDistribution object consists of parameters, a model
description, and sample data for a Rician probability distribution.

The Rician distribution is a continuous probability distribution that
models the magnitude of a signal in the presence of Gaussian noise. It is
defined by noncentrality parameter s and scale parameter sigma.

There are several ways to create a prob.RicianDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor
prob.RicianDistribution (s, sigma) to create a Rician
distribution with fixed parameter values s and sigma.
Use the static method prob.RicianDistribution.fit (x,
censor, freq, options) to fit a distribution to data
x.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the Rician distribution can be found at
https://en.wikipedia.org/wiki/Rice_distribution

See also:
fitdist,
makedist,
ricecdf,
riceinv,
ricepdf,
ricernd,
ricefit,
ricelike,
ricestat


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Rician probability distribution object.



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prob.RicianDistribution.DistributionName


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prob.RicianDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


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Probability distribution name



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prob.RicianDistribution.InputData


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prob.RicianDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


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Data used for fitting a probability distribution



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prob.RicianDistribution.IsTruncated


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prob.RicianDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


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Flag for truncated probability distribution



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prob.RicianDistribution.NumParameters


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prob.RicianDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


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Number of parameters



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prob.RicianDistribution.ParameterCovariance


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prob.RicianDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 2x2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


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Covariance matrix of the parameter estimates



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prob.RicianDistribution.ParameterDescription


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prob.RicianDistribution: property ParameterDescription
Description of parameters

A 2x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


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Description of parameters



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prob.RicianDistribution.ParameterIsFixed


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prob.RicianDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


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Flag for fixed parameters



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prob.RicianDistribution.ParameterNames


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prob.RicianDistribution: property ParameterNames
Names of parameters

A 2x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


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Names of parameters



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prob.RicianDistribution.ParameterValues


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prob.RicianDistribution: property ParameterValues
Distribution parameter values

A 2x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the s and sigma
properties.


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Distribution parameter values



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prob.RicianDistribution.RicianDistribution


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prob.RicianDistribution: pd = RicianDistribution (s, sigma)
prob.RicianDistribution: pd = RicianDistribution ()
Create a prob.RicianDistribution object.

s and sigma are the distribution parameters, which the class
help describes. Called with no arguments the parameters take their
defaults, s 1 and sigma 1.

makedist is the usual way to create a distribution object.


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Create a prob.RicianDistribution object.



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prob.RicianDistribution.Truncation


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prob.RicianDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


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Truncation interval



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prob.RicianDistribution.cdf


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prob.RicianDistribution: p = cdf (pd, x)
prob.RicianDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


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Compute the cumulative distribution function (CDF).



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prob.RicianDistribution.icdf


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prob.RicianDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


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Compute the inverse cumulative distribution function (iCDF).



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prob.RicianDistribution.iqr


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prob.RicianDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


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Compute the interquartile range of a probability distribution.



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prob.RicianDistribution.mean


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prob.RicianDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


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Compute the mean of a probability distribution.



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prob.RicianDistribution.median


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prob.RicianDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


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Compute the median of a probability distribution.



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prob.RicianDistribution.negloglik


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prob.RicianDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


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Compute the negative loglikelihood of a probability distribution.



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prob.RicianDistribution.paramci


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prob.RicianDistribution: ci = paramci (pd)
prob.RicianDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


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Compute the confidence intervals for probability distribution parameters.



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prob.RicianDistribution.pdf


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prob.RicianDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


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Compute the probability distribution function (PDF).



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prob.RicianDistribution.plot


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prob.RicianDistribution: plot (pd)
prob.RicianDistribution: plot (pd, Name, Value)
prob.RicianDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.RicianDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2031
prob.RicianDistribution: [nlogL, param] = proflik (pd, pnum)
prob.RicianDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.RicianDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.RicianDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.RicianDistribution: [nlogL, param] = proflik (pd)
prob.RicianDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the Rician distribution, pnum = 1 selects the
parameter s and pnum = 2 selects the parameter
sigma.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.RicianDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 683
prob.RicianDistribution: r = random (pd)
prob.RicianDistribution: r = random (pd, rows)
prob.RicianDistribution: r = random (pd, rows, cols, ...)
prob.RicianDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, ricernd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
prob.RicianDistribution.s


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 206
prob.RicianDistribution: property s
Noncentrality parameter

A non-negative scalar value characterizing the noncentrality of the
Rician distribution. You can access the s property using dot
name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 23
Noncentrality parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.RicianDistribution.sigma


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 194
prob.RicianDistribution: property sigma
Scale parameter

A positive scalar value characterizing the scale of the Rician
distribution. You can access the sigma property using dot name
assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.RicianDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 189
prob.RicianDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.RicianDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 532
prob.RicianDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower, and upper limit, upper. If pd is fitted to data
with fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.RicianDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 169
prob.RicianDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 23
prob.StableDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1756
statistics: prob.StableDistribution
Stable probability distribution object.

A prob.StableDistribution object consists of parameters, a model
description, and sample data for a stable probability distribution.

The stable distribution is a continuous probability distribution family
closed under linear combinations, generalizing the normal, Cauchy, and Levy
distributions. It is parameterized, in the Nolan S0
parameterization, by a tail index (first shape parameter) alpha in
(0, 2], a skewness (second shape parameter) beta in
[-1, 1], a scale parameter gam greater than zero, and a
location parameter delta.

There are several ways to create a prob.StableDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.StableDistribution (alpha,
beta, gam, delta) to create a stable distribution with
fixed parameter values alpha, beta, gam, and delta.
Use the static method prob.StableDistribution.fit (x,
alpha, freq, options) to fit a distribution to the data
in x using the same input arguments as the stblfit function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Fitting is by maximum likelihood. Because the stable density has no closed
form, it is evaluated by numerical inversion of the characteristic
function, which makes fitting considerably slower than for the closed-form
distributions.

Further information about the stable distribution can be found at
https://en.wikipedia.org/wiki/Stable_distribution

See also:
fitdist,
makedist,
stblpdf,
stblcdf,
stblinv,
stblrnd,
stblfit,
stbllike


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Stable probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.StableDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 188
prob.StableDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.StableDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 259
prob.StableDistribution: property InputData
Data used for fitting the distribution

A structure containing the data used to fit the distribution. It is
empty unless the distribution was fitted with fitdist or the
static fit method. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
Data used for fitting the distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.StableDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 172
prob.StableDistribution: property IsTruncated
Flag for truncated distribution

A logical scalar that is true when the distribution is truncated. This
property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
Flag for truncated distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.StableDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 201
prob.StableDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.StableDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 215
prob.StableDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 4x4 numeric matrix containing the variance-covariance of the
distribution parameters. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.StableDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 225
prob.StableDistribution: property ParameterDescription
Description of parameters

A 4x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.StableDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 193
prob.StableDistribution: property ParameterIsFixed
Flags for fixed parameters

A 4x1 logical vector specifying which parameters are held fixed
rather than estimated. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
Flags for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.StableDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 202
prob.StableDistribution: property ParameterNames
Names of parameters

A 4x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.StableDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 292
prob.StableDistribution: property ParameterValues
Distribution parameter values

A 4x1 numeric vector containing the values of the distribution
parameters, matching the order in ParameterNames. This property
is read-only; use dot name assignment on the alpha, beta,
gam, and delta properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.StableDistribution.StableDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 417
prob.StableDistribution: pd = StableDistribution (alpha, beta, gam, delta)
prob.StableDistribution: pd = StableDistribution ()
Create a prob.StableDistribution object.

alpha, beta, gam and delta are the distribution
parameters, which the class help describes. Called with no arguments the
parameters take their defaults, alpha 2, beta 0, gam 1
and delta 0.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
Create a prob.StableDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.StableDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 186
prob.StableDistribution: property Truncation
Truncation interval

A two-element numeric vector with the truncation interval, if the
distribution is truncated. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.StableDistribution.alpha


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 233
prob.StableDistribution: property alpha
Tail index (first shape parameter)

A scalar value in the range (0, 2] characterizing the tail
behaviour of the stable distribution. You can access the alpha
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
Tail index (first shape parameter)



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.StableDistribution.beta


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 225
prob.StableDistribution: property beta
Skewness (second shape parameter)

A scalar value in the range [-1, 1] characterizing the skewness of
the stable distribution. You can access the beta property using
dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
Skewness (second shape parameter)



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.StableDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 313
prob.StableDistribution: p = cdf (pd, x)
prob.StableDistribution: p = cdf (pd, x, "upper")
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x. The optional "upper" flag computes the upper tail
probability.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.StableDistribution.delta


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 191
prob.StableDistribution: property delta
Location parameter

A scalar value characterizing the location of the stable distribution.
You can access the delta property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
Location parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.StableDistribution.gam


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 190
prob.StableDistribution: property gam
Scale parameter

A positive scalar value characterizing the scale of the stable
distribution. You can access the gam property using dot name
assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.StableDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 241
prob.StableDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.StableDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 191
prob.StableDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.StableDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 218
prob.StableDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd. The mean is NaN for
alpha <= 1, where it is undefined.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.StableDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 171
prob.StableDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.StableDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 274
prob.StableDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd. It
returns an empty value when pd is not fitted to data.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.StableDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 988
prob.StableDistribution: ci = paramci (pd)
prob.StableDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise the parameter values are returned in both rows.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.StableDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 196
prob.StableDistribution: y = pdf (pd, x)
Compute the probability density function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the probability density function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.StableDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 362
prob.StableDistribution: plot (pd)
prob.StableDistribution: plot (pd, Name, Value)
prob.StableDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots the probability density function (PDF) of
the probability distribution object pd. Name-value pair arguments
select the plotted function and its appearance, as documented in
__plot__.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.StableDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1814
prob.StableDistribution: [nlogL, param] = proflik (pd, pnum)
prob.StableDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.StableDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.StableDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.StableDistribution: [nlogL, param] = proflik (pd)
prob.StableDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the stable distribution, pnum = 1 selects the tail
index alpha, pnum = 2 selects the skewness
beta, pnum = 3 selects the scale gam, and
pnum = 4 selects the location delta.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.StableDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 374
prob.StableDistribution: r = random (pd)
prob.StableDistribution: r = random (pd, rows)
prob.StableDistribution: r = random (pd, rows, cols, ...)
prob.StableDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd, following the size conventions of
stblrnd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.StableDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 246
prob.StableDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd. It is NaN for
alpha < 2, where the variance is infinite.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.StableDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 238
prob.StableDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns
the probability distribution pd truncated to the interval with
lower limit lower and upper limit upper.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.StableDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 226
prob.StableDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the probability
distribution object, pd. It is NaN for alpha <
2, where the variance is infinite.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 27
prob.TriangularDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 997
statistics: prob.TriangularDistribution
Triangular probability distribution object.

A prob.TriangularDistribution object consists of parameters, a model
description, and sample data for a triangular probability distribution.

The triangular distribution uses the following parameters.

Parameter Description Support
A Lower limit -Inf < A < Inf
B Peak location A <= B <= C
C Upper limit C > A

There are several ways to create a prob.TriangularDistribution
object.

Create a distribution with specified parameter values using the
makedist function.
Use the constructor
prob.TriangularDistribution (A, B, C) to create a
triangular distribution with specified parameter values A, B,
and C.

It is highly recommended to use makedist function to create
probability distribution objects, instead of the constructor.

Further information about the triangular distribution can be found
at https://en.wikipedia.org/wiki/Triangular_distribution

See also:
makedist,
tricdf,
triinv,
tripdf,
trirnd,
tristat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Triangular probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.TriangularDistribution.A


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 197
prob.TriangularDistribution: property A
Lower limit parameter

A scalar value characterizing the lower limit of the
triangular distribution. You can access the A
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 21
Lower limit parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.TriangularDistribution.B


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 201
prob.TriangularDistribution: property B
Peak location parameter

A scalar value characterizing the peak location of the
triangular distribution. You can access the B
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 23
Peak location parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.TriangularDistribution.C


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 197
prob.TriangularDistribution: property C
Upper limit parameter

A scalar value characterizing the upper limit of the
triangular distribution. You can access the C
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 21
Upper limit parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.TriangularDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 192
prob.TriangularDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.TriangularDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 212
prob.TriangularDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.TriangularDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 205
prob.TriangularDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.TriangularDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 229
prob.TriangularDistribution: property ParameterDescription
Description of parameters

A 3x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.TriangularDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 206
prob.TriangularDistribution: property ParameterNames
Names of parameters

A 3x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.TriangularDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 285
prob.TriangularDistribution: property ParameterValues
Distribution parameter values

A 3x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the A, B, and
C properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
prob.TriangularDistribution.TriangularDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 389
prob.TriangularDistribution: pd = TriangularDistribution (A, B, C)
prob.TriangularDistribution: pd = TriangularDistribution ()
Create a prob.TriangularDistribution object.

A, B and C are the distribution parameters, which the
class help describes. Called with no arguments the parameters take their
defaults, A 0, B 0.5 and C 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Create a prob.TriangularDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.TriangularDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 349
prob.TriangularDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.TriangularDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 390
prob.TriangularDistribution: p = cdf (pd, x)
prob.TriangularDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.TriangularDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 245
prob.TriangularDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.TriangularDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 195
prob.TriangularDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.TriangularDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 167
prob.TriangularDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.TriangularDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 175
prob.TriangularDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.TriangularDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 200
prob.TriangularDistribution: y = pdf (pd, x)
Compute the probability density function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the probability density function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.TriangularDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1110
prob.TriangularDistribution: plot (pd)
prob.TriangularDistribution: plot (pd, Name, Value)
prob.TriangularDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF).
'cdf' plots the cumulative density function (CDF).
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, this option is ignored.
'Parent' An axes graphics object for the plot.
If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.TriangularDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 698
prob.TriangularDistribution: r = random (pd)
prob.TriangularDistribution: r = random (pd, rows)
prob.TriangularDistribution: r = random (pd, rows, cols, ...)
prob.TriangularDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, trirnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.TriangularDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 193
prob.TriangularDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.TriangularDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 294
prob.TriangularDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower, and upper limit, upper.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.TriangularDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 173
prob.TriangularDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 24
prob.UniformDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1154
statistics: prob.UniformDistribution
Continuous uniform probability distribution object.

A prob.UniformDistribution object consists of parameters, a model
description, and sample data for a uniform probability distribution.

The uniform distribution is a continuous probability distribution that
models random variables that are equally likely to take any value within a
specified interval defined by the lower limit Lower and upper limit
Upper.

There are several ways to create a prob.UniformDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.UniformDistribution (Lower,
Upper) to create a uniform distribution with fixed parameter
values Lower and Upper.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor.

Further information about the continuous uniform distribution can be found
at https://en.wikipedia.org/wiki/Continuous_uniform_distribution

See also:
fitdist,
makedist,
unifcdf,
unifinv,
unifpdf,
unifrnd,
unifit,
unifstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Continuous uniform probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.UniformDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 189
prob.UniformDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.UniformDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 209
prob.UniformDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.UniformDistribution.Lower


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 199
prob.UniformDistribution: property Lower
Lower limit parameter

A scalar value characterizing the lower bound of the uniform
distribution. You can access the Lower property using dot
name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 21
Lower limit parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.UniformDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 202
prob.UniformDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.UniformDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 226
prob.UniformDistribution: property ParameterDescription
Description of parameters

A 2x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.UniformDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 203
prob.UniformDistribution: property ParameterNames
Names of parameters

A 2x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.UniformDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 286
prob.UniformDistribution: property ParameterValues
Distribution parameter values

A 2x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the Lower and Upper
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.UniformDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 346
prob.UniformDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.UniformDistribution.UniformDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 385
prob.UniformDistribution: pd = UniformDistribution (Lower, Upper)
prob.UniformDistribution: pd = UniformDistribution ()
Create a prob.UniformDistribution object.

Lower and Upper are the distribution parameters, which the
class help describes. Called with no arguments the parameters take their
defaults, Lower 0 and Upper 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
Create a prob.UniformDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 30
prob.UniformDistribution.Upper


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 199
prob.UniformDistribution: property Upper
Upper limit parameter

A scalar value characterizing the upper bound of the uniform
distribution. You can access the Upper property using dot
name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 21
Upper limit parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.UniformDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 384
prob.UniformDistribution: p = cdf (pd, x)
prob.UniformDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.UniformDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 242
prob.UniformDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.UniformDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 192
prob.UniformDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.UniformDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 164
prob.UniformDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.UniformDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 172
prob.UniformDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.UniformDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 202
prob.UniformDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.UniformDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1519
prob.UniformDistribution: plot (pd)
prob.UniformDistribution: plot (pd, Name, Value)
prob.UniformDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.UniformDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 687
prob.UniformDistribution: r = random (pd)
prob.UniformDistribution: r = random (pd, rows)
prob.UniformDistribution: r = random (pd, rows, cols, ...)
prob.UniformDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, unifrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.UniformDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 190
prob.UniformDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.UniformDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 533
prob.UniformDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower, and upper limit, upper. If pd is fitted to data
with fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.UniformDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 170
prob.UniformDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 24
prob.WeibullDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1459
statistics: prob.WeibullDistribution
Weibull probability distribution object.

A prob.WeibullDistribution object consists of parameters, a model
description, and sample data for a Weibull probability distribution.

The Weibull distribution is a continuous probability distribution that
models the time to failure of materials or the lifetime of mechanical
systems. It is defined by scale parameter A and shape
parameter B.

A is the lambda of the usual mathematical notation and
B is its k. The wbl* functions name the same two
quantities lambda and k; this class follows MATLAB.

There are several ways to create a prob.WeibullDistribution object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.WeibullDistribution (A,
B) to create a Weibull distribution with fixed parameter
values A and B.
Use the static method prob.WeibullDistribution.fit (x,
alpha, censor, freq) to fit a distribution to the
data in x using the same input arguments as the wblfit
function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the Weibull distribution can be found at
https://en.wikipedia.org/wiki/Weibull_distribution

See also:
fitdist,
makedist,
wblcdf,
wblinv,
wblpdf,
wblrnd,
wblfit,
wbllike,
wblstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
Weibull probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.WeibullDistribution.A


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 188
prob.WeibullDistribution: property A
Scale parameter

A positive scalar value characterizing the scale of the
Weibull distribution. You can access the A
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 26
prob.WeibullDistribution.B


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 188
prob.WeibullDistribution: property B
Shape parameter

A positive scalar value characterizing the shape of the
Weibull distribution. You can access the B
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Shape parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.WeibullDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 189
prob.WeibullDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.WeibullDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 736
prob.WeibullDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.WeibullDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 209
prob.WeibullDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.WeibullDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 202
prob.WeibullDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.WeibullDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 615
prob.WeibullDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 2x2 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.WeibullDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 226
prob.WeibullDistribution: property ParameterDescription
Description of parameters

A 2x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.WeibullDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 282
prob.WeibullDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x2 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.WeibullDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 203
prob.WeibullDistribution: property ParameterNames
Names of parameters

A 2x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.WeibullDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 278
prob.WeibullDistribution: property ParameterValues
Distribution parameter values

A 2x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the A and B
properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.WeibullDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 346
prob.WeibullDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
prob.WeibullDistribution.WeibullDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 361
prob.WeibullDistribution: pd = WeibullDistribution (A, B)
prob.WeibullDistribution: pd = WeibullDistribution ()
Create a prob.WeibullDistribution object.

A and B are the distribution parameters, which the class help
describes. Called with no arguments the parameters take their defaults,
A 1 and B 1.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
Create a prob.WeibullDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.WeibullDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 384
prob.WeibullDistribution: p = cdf (pd, x)
prob.WeibullDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.WeibullDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 242
prob.WeibullDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.WeibullDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 192
prob.WeibullDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.WeibullDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 164
prob.WeibullDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.WeibullDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 172
prob.WeibullDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.WeibullDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 218
prob.WeibullDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.WeibullDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 975
prob.WeibullDistribution: ci = paramci (pd)
prob.WeibullDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.WeibullDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 202
prob.WeibullDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
prob.WeibullDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1519
prob.WeibullDistribution: plot (pd)
prob.WeibullDistribution: plot (pd, Name, Value)
prob.WeibullDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 32
prob.WeibullDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2034
prob.WeibullDistribution: [nlogL, param] = proflik (pd, pnum)
prob.WeibullDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.WeibullDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.WeibullDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.WeibullDistribution: [nlogL, param] = proflik (pd)
prob.WeibullDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the Weibull distribution, pnum = 1 selects the
parameter A and pnum = 2 selects the
parameter B.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.WeibullDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 686
prob.WeibullDistribution: r = random (pd)
prob.WeibullDistribution: r = random (pd, rows)
prob.WeibullDistribution: r = random (pd, rows, cols, ...)
prob.WeibullDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, wblrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.WeibullDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 190
prob.WeibullDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
prob.WeibullDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 533
prob.WeibullDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower, and upper limit, upper. If pd is fitted to data
with fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 28
prob.WeibullDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 170
prob.WeibullDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 31
prob.tLocationScaleDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1536
statistics: prob.tLocationScaleDistribution
Location-Scale Student's T probability distribution object.

A prob.tLocationScaleDistribution object consists of parameters, a
model description, and sample data for a location-scale Student's T
probability distribution.

The location-scale Student's T distribution is a continuous probability
distribution that generalizes the standard Student's T distribution by
including location and scale parameters. It is defined by location
parameter
mu, scale parameter sigma, and degrees of freedom nu.

There are several ways to create a prob.tLocationScaleDistribution
object.

Fit a distribution to data using the fitdist function.
Create a distribution with fixed parameter values using the
makedist function.
Use the constructor prob.tLocationScaleDistribution (mu,
sigma, nu) to create a location-scale Student's T distribution
with fixed parameter values mu, sigma, and nu.
Use the static method prob.tLocationScaleDistribution.fit
(x, censor, freq, options) to fit a distribution
to the data in x using the same input arguments as the tlsfit
function.

It is highly recommended to use fitdist and makedist
functions to create probability distribution objects, instead of the class
constructor or the aforementioned static method.

Further information about the location-scale Student's T distribution can
be found at
https://en.wikipedia.org/wiki/Student%27s_t-distribution#Location-scale_t_distribution

See also:
fitdist,
makedist,
tlscdf,
tlsinv,
tlspdf,
tlsrnd,
tlsfit,
tlslike,
tlsstat


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 59
Location-Scale Student's T probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.tLocationScaleDistribution.DistributionName


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 196
prob.tLocationScaleDistribution: property DistributionName
Probability distribution name

A character vector specifying the name of the probability distribution
object. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Probability distribution name



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.tLocationScaleDistribution.InputData


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 743
prob.tLocationScaleDistribution: property InputData
Data used for fitting a probability distribution

A scalar structure containing the following fields:

data: a numeric vector containing the data used for
distribution fitting.
cens: a numeric vector of logical values indicating
censoring information corresponding to the elements of the data used for
distribution fitting. If no censoring vector was used for distribution
fitting, then this field defaults to an empty array.
freq: a numeric vector of non-negative integer values
containing the frequency information corresponding to the elements of the
data used for distribution fitting. If no frequency vector was used for
distribution fitting, then this field defaults to an empty array.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Data used for fitting a probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
prob.tLocationScaleDistribution.IsTruncated


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 216
prob.tLocationScaleDistribution: property IsTruncated
Flag for truncated probability distribution

A logical scalar value specifying whether a probability distribution is
truncated or not. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 43
Flag for truncated probability distribution



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 45
prob.tLocationScaleDistribution.NumParameters


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 209
prob.tLocationScaleDistribution: property NumParameters
Number of parameters

A scalar integer value specifying the number of parameters characterizing
the probability distribution. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 20
Number of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
prob.tLocationScaleDistribution.ParameterCovariance


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 622
prob.tLocationScaleDistribution: property ParameterCovariance
Covariance matrix of the parameter estimates

A 3x3 numeric matrix containing the variance-covariance of the
parameter estimates. Diagonal elements contain the variance of each
estimated parameter, and non-diagonal elements contain the covariance
between the parameter estimates. The covariance matrix is only
meaningful when the distribution was fitted to data. If the distribution
object was created with fixed parameters, or a parameter of a fitted
distribution is modified, then all elements of the variance-covariance
are zero. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 44
Covariance matrix of the parameter estimates



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
prob.tLocationScaleDistribution.ParameterDescription


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 233
prob.tLocationScaleDistribution: property ParameterDescription
Description of parameters

A 3x1 cell array of character vectors with each element containing
a short description of a distribution parameter. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Description of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
prob.tLocationScaleDistribution.ParameterIsFixed


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 289
prob.tLocationScaleDistribution: property ParameterIsFixed
Flag for fixed parameters

A 1x3 logical vector specifying which parameters are fixed and
which are estimated. true values correspond to fixed parameters,
false values correspond to parameter estimates. This property is
read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 25
Flag for fixed parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 46
prob.tLocationScaleDistribution.ParameterNames


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 210
prob.tLocationScaleDistribution: property ParameterNames
Names of parameters

A 3x1 cell array of character vectors with each element containing
the name of a distribution parameter. This property is read-only.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Names of parameters



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
prob.tLocationScaleDistribution.ParameterValues


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 295
prob.tLocationScaleDistribution: property ParameterValues
Distribution parameter values

A 3x1 numeric vector containing the values of the distribution
parameters. This property is read-only. You can change the distribution
parameters by assigning new values to the mu, sigma, and
nu properties.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 29
Distribution parameter values



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
prob.tLocationScaleDistribution.Truncation


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 353
prob.tLocationScaleDistribution: property Truncation
Truncation interval

A 1x2 numeric vector specifying the truncation interval for the
probability distribution. First element contains the lower boundary,
second element contains the upper boundary. This property is read-only.
You can only truncate a probability distribution with the
truncate method.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 19
Truncation interval



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.tLocationScaleDistribution.cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 398
prob.tLocationScaleDistribution: p = cdf (pd, x)
prob.tLocationScaleDistribution: p = cdf (pd, x, 'upper')
Compute the cumulative distribution function (CDF).

p = cdf (pd, x) computes the CDF of the
probability distribution object, pd, evaluated at the values in
x.

p = cdf (..., 'upper') returns the complement of
the CDF of the probability distribution object, pd, evaluated at
the values in x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the cumulative distribution function (CDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.tLocationScaleDistribution.icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 249
prob.tLocationScaleDistribution: x = icdf (pd, p)
Compute the inverse cumulative distribution function (iCDF).

x = icdf (pd, p) computes the quantile (the
inverse of the CDF) of the probability distribution object, pd,
evaluated at the values in p.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 60
Compute the inverse cumulative distribution function (iCDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.tLocationScaleDistribution.iqr


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 199
prob.tLocationScaleDistribution: r = iqr (pd)
Compute the interquartile range of a probability distribution.

r = iqr (pd) computes the interquartile range of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Compute the interquartile range of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.tLocationScaleDistribution.mean


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 171
prob.tLocationScaleDistribution: m = mean (pd)
Compute the mean of a probability distribution.

m = mean (pd) computes the mean of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 47
Compute the mean of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.tLocationScaleDistribution.median


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 179
prob.tLocationScaleDistribution: m = median (pd)
Compute the median of a probability distribution.

m = median (pd) computes the median of the probability
distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Compute the median of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.tLocationScaleDistribution.mu


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 213
prob.tLocationScaleDistribution: property mu
Location parameter

A scalar value characterizing the location of the
location-scale Student's T distribution. You can access the mu
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
Location parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
prob.tLocationScaleDistribution.negloglik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 225
prob.tLocationScaleDistribution: nlogL = negloglik (pd)
Compute the negative loglikelihood of a probability distribution.

nlogL = negloglik (pd) computes the negative
loglikelihood of the probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Compute the negative loglikelihood of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 34
prob.tLocationScaleDistribution.nu


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 232
prob.tLocationScaleDistribution: property nu
Degrees of freedom

A positive scalar value characterizing the degrees of freedom of the
location-scale Student's T distribution. You can access the nu
property using dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 18
Degrees of freedom



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.tLocationScaleDistribution.paramci


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 989
prob.tLocationScaleDistribution: ci = paramci (pd)
prob.tLocationScaleDistribution: ci = paramci (pd, Name, Value)
Compute the confidence intervals for probability distribution parameters.

ci = paramci (pd) computes the lower and upper
boundaries of the 95% confidence interval for each parameter of the
probability distribution object, pd.

ci = paramci (pd, Name, Value) computes
the confidence intervals with additional options specified by
Name-Value pair arguments listed below.

Name Value
'Alpha' A scalar value in the range (0,1)
specifying the significance level for the confidence interval. The
default value 0.05 corresponds to a 95% confidence interval.
'Parameter' A character vector or a cell array of
character vectors specifying the parameter names for which to compute
confidence intervals. By default, paramci computes confidence
intervals for all distribution parameters.

paramci is meaningful only when pd is fitted to data,
otherwise an empty array, [], is returned.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 73
Compute the confidence intervals for probability distribution parameters.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.tLocationScaleDistribution.pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 209
prob.tLocationScaleDistribution: y = pdf (pd, x)
Compute the probability distribution function (PDF).

y = pdf (pd, x) computes the PDF of the
probability distribution object, pd, evaluated at the values in
x.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Compute the probability distribution function (PDF).



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
prob.tLocationScaleDistribution.plot


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1540
prob.tLocationScaleDistribution: plot (pd)
prob.tLocationScaleDistribution: plot (pd, Name, Value)
prob.tLocationScaleDistribution: h = plot (...)
Plot a probability distribution object.

plot (pd) plots a probability density function (PDF) of the
probability distribution object pd. If pd contains data,
which have been fitted by fitdist, the PDF is superimposed over a
histogram of the data.

plot (pd, Name, Value) specifies additional
options with the Name-Value pair arguments listed below.

Name Value
'PlotType' A character vector specifying the plot
type. 'pdf' plots the probability density function (PDF). When
pd is fit to data, the PDF is superimposed on a histogram of the
data. 'cdf' plots the cumulative density function (CDF). When
pd is fit to data, the CDF is superimposed over an empirical CDF.
'probability' plots a probability plot using a CDF of the data
and a CDF of the fitted probability distribution. This option is
available only when pd is fitted to data.
'Discrete' A logical scalar to specify whether to
plot the PDF or CDF of a discrete distribution object as a line plot or a
stem plot, by specifying false or true, respectively. By
default, it is true for discrete distributions and false
for continuous distributions. When pd is a continuous distribution
object, option is ignored.
'Parent' An axes graphics object for plot. If
not specified, the plot function plots into the current axes or
creates a new axes object if one does not exist.

h = plot (...) returns a graphics handle to the plotted
objects.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
Plot a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
prob.tLocationScaleDistribution.proflik


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2136
prob.tLocationScaleDistribution: [nlogL, param] = proflik (pd, pnum)
prob.tLocationScaleDistribution: [nlogL, param] = proflik (pd, pnum, 'Display', display)
prob.tLocationScaleDistribution: [nlogL, param] = proflik (pd, pnum, setparam)
prob.tLocationScaleDistribution: [nlogL, param] = proflik (pd, pnum, setparam, 'Display', display)
prob.tLocationScaleDistribution: [nlogL, param] = proflik (pd)
prob.tLocationScaleDistribution: [nlogL, param, other] = proflik (...)
Profile likelihood function for a probability distribution object.

[nlogL, param] = proflik (pd, pnum)
returns a vector nlogL of negative loglikelihood values and a
vector param of corresponding parameter values for the parameter in
the position indicated by pnum. By default, proflik uses
the lower and upper bounds of the 98% confidence interval and computes
101 equispaced values for the selected parameter when it is the only one
being estimated, and 21 values otherwise. pd must be fitted to
data.

[nlogL, param] = proflik (pd, pnum,
'Display', 'on') also plots the profile likelihood
against the default range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam) defines a user-defined range of the selected parameter.

[nlogL, param] = proflik (pd, pnum,
setparam, 'Display', 'on') also plots the profile
likelihood against the user-defined range of the selected parameter.

[nlogL, param] = proflik (pd) selects the
first parameter that is not fixed.

[nlogL, param, other] = proflik (...) also
returns a matrix other holding, in each row, the values of the
remaining parameters that maximize the likelihood at the corresponding
value of param. A fixed parameter keeps its own value.

For the location-scale Student's T distribution, pnum = 1
selects the parameter mu, pnum = 2 selects the
parameter sigma, and pnum = 3 selects the
parameter nu.

When opted to display the profile likelihood plot, proflik also
plots the baseline loglikelihood computed at the lower bound of the 95%
confidence interval and estimated maximum likelihood. The latter might
not be observable if it is outside of the used-defined range of parameter
values.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 66
Profile likelihood function for a probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 38
prob.tLocationScaleDistribution.random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 714
prob.tLocationScaleDistribution: r = random (pd)
prob.tLocationScaleDistribution: r = random (pd, rows)
prob.tLocationScaleDistribution: r = random (pd, rows, cols, ...)
prob.tLocationScaleDistribution: r = random (pd, [sz])
Generate random arrays from the probability distribution object.

r = random (pd) returns a random number from the
distribution object pd.

When called with a single size argument, tlsrnd returns a square
matrix with the dimension specified. When called with more than one
scalar argument, the first two arguments are taken as the number of rows
and columns and any further arguments specify additional matrix
dimensions. The size may also be specified with a row vector of
dimensions, sz.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Generate random arrays from the probability distribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
prob.tLocationScaleDistribution.sigma


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 222
prob.tLocationScaleDistribution: property sigma
Scale parameter

A positive scalar value characterizing the scale of the location-scale
Student's T distribution. You can access the sigma property using
dot name assignment.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 15
Scale parameter



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.tLocationScaleDistribution.std


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 197
prob.tLocationScaleDistribution: s = std (pd)
Compute the standard deviation of a probability distribution.

s = std (pd) computes the standard deviation of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 61
Compute the standard deviation of a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 58
prob.tLocationScaleDistribution.tLocationScaleDistribution


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 425
prob.tLocationScaleDistribution: pd = tLocationScaleDistribution (mu, sigma, nu)
prob.tLocationScaleDistribution: pd = tLocationScaleDistribution ()
Create a prob.tLocationScaleDistribution object.

mu, sigma and nu are the distribution parameters, which
the class help describes. Called with no arguments the parameters take
their defaults, mu 0, sigma 1 and nu 5.

makedist is the usual way to create a distribution object.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 48
Create a prob.tLocationScaleDistribution object.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 40
prob.tLocationScaleDistribution.truncate


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 540
prob.tLocationScaleDistribution: t = truncate (pd, lower, upper)
Truncate a probability distribution.

t = truncate (pd, lower, upper) returns a
probability distribution t, which is the probability distribution
pd truncated to the specified interval with lower limit,
lower, and upper limit, upper. If pd is fitted to data
with fitdist, the returned probability distribution t is not
fitted, does not contain any data or estimated values, and it is as it
has been created with the makedist function, but it includes the
truncation interval.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 36
Truncate a probability distribution.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 35
prob.tLocationScaleDistribution.var


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 177
prob.tLocationScaleDistribution: v = var (pd)
Compute the variance of a probability distribution.

v = var (pd) computes the variance of the
probability distribution object, pd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 51
Compute the variance of a probability distribution.





