# doc-cache created by Octave 11.2.0
# name: cache
# type: cell
# rows: 3
# columns: 8
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3
cdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5133
 -- statistics: P = cdf (NAME, X, A)
 -- statistics: P = cdf (NAME, X, A, B)
 -- statistics: P = cdf (NAME, X, A, B, C)
 -- statistics: P = cdf (..., 'upper')

     Return the CDF of a univariate distribution evaluated at X.

     ‘cdf’ is a wrapper for the univariate cumulative distribution functions
     available in the statistics package.  See the corresponding functions' help
     to learn the signification of the parameters after X.

     ‘P = cdf (NAME, X, A)’ returns the CDF for the one-parameter distribution
     family specified by NAME and the distribution parameter A, evaluated at the
     values in X.

     ‘P = cdf (NAME, X, A, B)’ returns the CDF for the two-parameter
     distribution family specified by NAME and the distribution parameters A and
     B, evaluated at the values in X.

     ‘P = cdf (NAME, X, A, B, C)’ returns the CDF for the three-parameter
     distribution family specified by NAME and the distribution parameters A, B,
     and C, evaluated at the values in X.

     ‘P = cdf (..., 'upper')’ returns the complement of the CDF using an
     algorithm that more accurately computes the extreme upper-tail
     probabilities.  'upper' can follow any of the input arguments in the
     previous syntaxes.

     NAME must be a char string of the name or the abbreviation of the desired
     cumulative distribution function as listed in the following table.  The
     last column shows the number of required parameters that should be parsed
     after X to the desired CDF. The optional input argument 'upper' does not
     count in the required number of parameters.

     Distribution Name                Abbreviation     Input Parameters
     ---------------------------------------------------------------------------
     'Beta'                           'beta'           2
     'Binomial'                       'bino'           2
     'Birnbaum-Saunders'              'bisa'           2
     'Burr'                           'burr'           3
     'Cauchy'                         'cauchy'         2
     'Chi-squared'                    'chi2'           1
     'Extreme Value'                  'ev'             2
     'Exponential'                    'exp'            1
     'F-Distribution'                 'f'              2
     'Gamma'                          'gam'            2
     'Geometric'                      'geo'            1
     'Generalized Extreme Value'      'gev'            3
     'Generalized Pareto'             'gp'             3
     'Gumbel'                         'gumbel'         2
     'Half-normal'                    'hn'             2
     'Hypergeometric'                 'hyge'           3
     'Inverse Gaussian'               'invg'           2
     'Laplace'                        'laplace'        2
     'Logistic'                       'logi'           2
     'Log-Logistic'                   'logl'           2
     'Lognormal'                      'logn'           2
     'Nakagami'                       'naka'           2
     'Negative Binomial'              'nbin'           2
     'Noncentral F-Distribution'      'ncf'            3
     'Noncentral Student T'           'nct'            2
     'Noncentral Chi-Squared'         'ncx2'           2
     'Normal'                         'norm'           2
     'Poisson'                        'poiss'          1
     'Rayleigh'                       'rayl'           1
     'Rician'                         'rice'           2
     'Student T'                      't'              1
     'location-scale T'               'tls'            3
     'Triangular'                     'tri'            3
     'Discrete Uniform'               'unid'           1
     'Uniform'                        'unif'           2
     'Von Mises'                      'vm'             2
     'Weibull'                        'wbl'            2

     Distribution names are matched ignoring case, spaces and hyphens, so that
     'Extreme Value', 'ExtremeValue' and 'extreme-value' all select the same
     distribution, and the same set of names is accepted by ‘cdf’, ‘pdf’,
     ‘icdf’, ‘random’, ‘makedist’, ‘fitdist’ and ‘mle’.

     This accepts more names than MATLAB. MATLAB takes the spaced and the
     squashed spelling but refuses the hyphenated one, so 'Birnbaum-Saunders'
     and 'Log-Logistic' are errors there; Octave has always accepted them and
     continues to.  MATLAB also accepts 'tLocationScale' in ‘makedist’ while
     refusing it in ‘cdf’ for the same distribution; Octave accepts it, and
     'location-scale T', everywhere.  Code written against MATLAB's names
     therefore runs unchanged, but code relying on these names will not port
     back.

     See also: icdf, pdf, cdf, betacdf, binocdf, bisacdf, burrcdf, cauchycdf,
     chi2cdf, evcdf, expcdf, fcdf, gamcdf, geocdf, gevcdf, gpcdf, gumbelcdf,
     hncdf, hygecdf, invgcdf, laplacecdf, logicdf, loglcdf, logncdf, nakacdf,
     nbincdf, ncfcdf, nctcdf, ncx2cdf, normcdf, poisscdf, raylcdf, ricecdf,
     tcdf, tlscdf, tricdf, unidcdf, unifcdf, vmcdf, wblcdf.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 59
Return the CDF of a univariate distribution evaluated at X.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
fitdist


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3958
 -- statistics: PD = fitdist (X, DISTNAME)
 -- statistics: PD = fitdist (X, DISTNAME, NAME, VALUE)
 -- statistics: [PDCA, GN, GL] = fitdist (X, DISTNAME, 'By', GROUPVAR)
 -- statistics: [PDCA, GN, GL] = fitdist (X, DISTNAME, 'By', GROUPVAR, NAME,
          VALUE)

     Create probability distribution object.

     ‘PD = fitdist (X, DISTNAME)’ creates a probability distribution object by
     fitting the distribution specified by DISTNAME to the data in vector X.

     ‘PD = fitdist (X, DISTNAME, NAME, VALUE)’ creates the probability
     distribution object with additional options specified by one or more
     Name-Value pair arguments listed below.

     NAME           VALUE
                    
     --------------------------------------------------------------------------------
     'distribution' A character vector specifying the distribution type for which
                    to estimate parameters.
                    
     'Ntrials'      A scalar specifying the number of trials for the corresponding
                    element of X for the binomial distribution.
                    
     'theta'        A scalar specifying the location parameter for the generalized
                    Pareto distribution.  It defaults to 0, as MATLAB assumes it,
                    and is not estimated.
                    
     'mu'           A scalar specifying the location parameter for the half-normal
                    distribution.
                    
     'censoring'    A vector of the same size as X indicating censored data in X.
                    By default it is CENSOR = zeros (size (X)).
                    
     'frequency'    A vector of nonnegative integer counts of the same size as X
                    used as frequency observations.  By default it is FREQ = ones
                    (size (X)).
                    
     'alpha'        A scalar in the range (0,1), as the significance level for the
                    confidence interval PCI.  By default it is 0.05 corresponding
                    to 95% confidence intervals.
                    
     'options'      A structure specifying the control parameters for the
                    iterative algorithm used to compute ML estimates with the
                    ‘fminsearch’ function.

     ‘[PDCA, GN, GL] = fitdist (X, DISTNAME, 'By', GROUPVAR)’ creates
     probability distribution objects by fitting the distribution specified by
     DISTNAME to the data in X based on the grouping variable GROUPVAR.  It
     returns a cell array of fitted probability distribution object, PDCA, a
     cell array of group labels, GN, and a cell array of grouping variable
     levels, GL.

     ‘[PDCA, GN, GL] = fitdist (X, DISTNAME, 'By', GROUPVAR, NAME, VALUE)’
     returns the same output arguments using additional options specified by one
     or more Name-Value pair arguments mentioned above.

     Note: calling ‘fitdist’ without any input arguments will return a cell
     array of character vectors listing all supported distributions.

     Distribution names are matched ignoring case, spaces and hyphens, so that
     'Extreme Value', 'ExtremeValue' and 'extreme-value' all select the same
     distribution, and the same set of names is accepted by ‘cdf’, ‘pdf’,
     ‘icdf’, ‘random’, ‘makedist’, ‘fitdist’ and ‘mle’.

     This accepts more names than MATLAB. MATLAB takes the spaced and the
     squashed spelling but refuses the hyphenated one, so 'Birnbaum-Saunders'
     and 'Log-Logistic' are errors there; Octave has always accepted them and
     continues to.  MATLAB also accepts 'tLocationScale' in ‘makedist’ while
     refusing it in ‘cdf’ for the same distribution; Octave accepts it, and
     'location-scale T', everywhere.  Code written against MATLAB's names
     therefore runs unchanged, but code relying on these names will not port
     back.

     See also: makedist.


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



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
icdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4781
 -- statistics: X = icdf (NAME, P, A)
 -- statistics: X = icdf (NAME, P, A, B)
 -- statistics: X = icdf (NAME, P, A, B, C)

     Return the inverse CDF of a univariate distribution evaluated at P.

     ‘icdf’ is a wrapper for the univariate quantile distribution functions
     (iCDF) available in the statistics package.  See the corresponding
     functions' help to learn the signification of the parameters after P.

     ‘X = icdf (NAME, P, A)’ returns the iCDF for the one-parameter distribution
     family specified by NAME and the distribution parameter A, evaluated at the
     values in P.

     ‘X = icdf (NAME, P, A, B)’ returns the iCDF for the two-parameter
     distribution family specified by NAME and the distribution parameters A and
     B, evaluated at the values in P.

     ‘X = icdf (NAME, P, A, B, C)’ returns the iCDF for the three-parameter
     distribution family specified by NAME and the distribution parameters A, B,
     and C, evaluated at the values in P.

     NAME must be a char string of the name or the abbreviation of the desired
     quantile distribution function as listed in the following table.  The last
     column shows the number of required parameters that should be parsed after
     X to the desired iCDF.

     Distribution Name                Abbreviation     Input Parameters
     ---------------------------------------------------------------------------
     'Beta'                           'beta'           2
     'Binomial'                       'bino'           2
     'Birnbaum-Saunders'              'bisa'           2
     'Burr'                           'burr'           3
     'Cauchy'                         'cauchy'         2
     'Chi-squared'                    'chi2'           1
     'Extreme Value'                  'ev'             2
     'Exponential'                    'exp'            1
     'F-Distribution'                 'f'              2
     'Gamma'                          'gam'            2
     'Geometric'                      'geo'            1
     'Generalized Extreme Value'      'gev'            3
     'Generalized Pareto'             'gp'             3
     'Gumbel'                         'gumbel'         2
     'Half-normal'                    'hn'             2
     'Hypergeometric'                 'hyge'           3
     'Inverse Gaussian'               'invg'           2
     'Laplace'                        'laplace'        2
     'Logistic'                       'logi'           2
     'Log-Logistic'                   'logl'           2
     'Lognormal'                      'logn'           2
     'Nakagami'                       'naka'           2
     'Negative Binomial'              'nbin'           2
     'Noncentral F-Distribution'      'ncf'            3
     'Noncentral Student T'           'nct'            2
     'Noncentral Chi-Squared'         'ncx2'           2
     'Normal'                         'norm'           2
     'Poisson'                        'poiss'          1
     'Rayleigh'                       'rayl'           1
     'Rician'                         'rice'           2
     'Student T'                      't'              1
     'location-scale T'               'tls'            3
     'Triangular'                     'tri'            3
     'Discrete Uniform'               'unid'           1
     'Uniform'                        'unif'           2
     'Von Mises'                      'vm'             2
     'Weibull'                        'wbl'            2

     Distribution names are matched ignoring case, spaces and hyphens, so that
     'Extreme Value', 'ExtremeValue' and 'extreme-value' all select the same
     distribution, and the same set of names is accepted by ‘cdf’, ‘pdf’,
     ‘icdf’, ‘random’, ‘makedist’, ‘fitdist’ and ‘mle’.

     This accepts more names than MATLAB. MATLAB takes the spaced and the
     squashed spelling but refuses the hyphenated one, so 'Birnbaum-Saunders'
     and 'Log-Logistic' are errors there; Octave has always accepted them and
     continues to.  MATLAB also accepts 'tLocationScale' in ‘makedist’ while
     refusing it in ‘cdf’ for the same distribution; Octave accepts it, and
     'location-scale T', everywhere.  Code written against MATLAB's names
     therefore runs unchanged, but code relying on these names will not port
     back.

     See also: icdf, pdf, random, betainv, binoinv, bisainv, burrinv, cauchyinv,
     chi2inv, evinv, expinv, finv, gaminv, geoinv, gevinv, gpinv, gumbelinv,
     hninv, hygeinv, invginv, laplaceinv, logiinv, loglinv, logninv, nakainv,
     nbininv, ncfinv, nctinv, ncx2inv, norminv, poissinv, raylinv, riceinv,
     tinv, tlsinv, triinv, unidinv, unifinv, vminv, wblinv.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 67
Return the inverse CDF of a univariate distribution evaluated at P.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
makedist


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1562
 -- statistics: PD = makedist (DISTNAME)
 -- statistics: PD = makedist (DISTNAME, NAME, VALUE)
 -- statistics: LIST = makedist

     Create probability distribution object.

     ‘PD = makedist (DISTNAME)’ creates a probability distribution object for
     the distribution specified in DISTNAME, using the default parameter values.

     ‘PD = makedist (DISTNAME, NAME, VALUE)’ also creates a probability
     distribution object with one or more distribution parameter values
     specified by Name-Value pair arguments.

     ‘LIST = makedist’ returns a cell array, LIST, containing a list of the
     probability distributions that makedist can create.

     Distribution names are matched ignoring case, spaces and hyphens, so that
     'Extreme Value', 'ExtremeValue' and 'extreme-value' all select the same
     distribution, and the same set of names is accepted by ‘cdf’, ‘pdf’,
     ‘icdf’, ‘random’, ‘makedist’, ‘fitdist’ and ‘mle’.

     This accepts more names than MATLAB. MATLAB takes the spaced and the
     squashed spelling but refuses the hyphenated one, so 'Birnbaum-Saunders'
     and 'Log-Logistic' are errors there; Octave has always accepted them and
     continues to.  MATLAB also accepts 'tLocationScale' in ‘makedist’ while
     refusing it in ‘cdf’ for the same distribution; Octave accepts it, and
     'location-scale T', everywhere.  Code written against MATLAB's names
     therefore runs unchanged, but code relying on these names will not port
     back.

     See also: fitdist.


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



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3
mle


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 5826
 -- statistics: PHAT = mle (X)
 -- statistics: PHAT = mle (X, NAME, VALUE)
 -- statistics: [PHAT, PCI] = mle (...)

     Compute maximum likelihood estimates.

     ‘PHAT = mle (X)’ returns the maximum likelihood estimates (MLEs) for the
     parameters of a normal distribution using the sample data in X, which must
     be a numeric vector of real values.

     ‘PHAT = mle (X, NAME, VALUE)’ returns the MLEs with additional options
     specified by Name-Value pair arguments listed below.

     NAME           VALUE
                    
     --------------------------------------------------------------------------------
     'distribution' A character vector specifying the distribution type for which
                    to estimate parameters.
                    
     'Ntrials'      A scalar specifying the number of trials for the corresponding
                    element of X for the binomial distribution.
                    
     'theta'        A scalar specifying the location parameter for the generalized
                    Pareto distribution.  It defaults to 0 and is not estimated:
                    the data is shifted by it and only K and SIGMA are returned.
                    
     'mu'           A scalar specifying the location parameter for the half-normal
                    distribution.
                    
     'censoring'    A vector of the same size as X indicating censored data in X.
                    By default it is CENSOR = zeros (size (X)).
                    
     'frequency'    A vector of nonnegative integer counts of the same size as X
                    used as frequency observations.  By default it is FREQ = ones
                    (size (X)).
                    
     'alpha'        A scalar in the range (0,1), as the significance level for the
                    confidence interval PCI.  By default it is 0.05 corresponding
                    to 95% confidence intervals.
                    
     'options'      A structure specifying the control parameters for the
                    iterative algorithm used to compute ML estimates with the
                    ‘fminsearch’ function.
                    
     'pdf'          A function handle ‘@(DATA, P1, P2, ...)’ to the probability
                    density of a *custom* distribution, whose parameters are then
                    estimated by maximum likelihood.  Requires 'start'.  It is
                    mutually exclusive with 'distribution' and with
                    'logpdf'/'nloglf'.
                    
     'cdf'          A function handle to the cumulative distribution function of
                    the custom distribution, with the same calling convention as
                    'pdf'.  Required together with 'pdf' for censored or truncated
                    data.
                    
     'logpdf'       A function handle to the log probability density of a custom
                    distribution, with the same calling convention as 'pdf'.
                    Requires 'start'.
                    
     'logsf'        A function handle to the log survivor function log (1 - cdf)
                    of the custom distribution, with the same calling convention
                    as 'pdf'.  Required together with 'logpdf' for censored data.
                    
     'nloglf'       A function handle ‘@(PARAMS, DATA, CENS, FREQ)’ returning the
                    scalar negative log-likelihood of a custom distribution.
                    Requires 'start'.
                    
     'start'        A vector of initial parameter values for a custom-distribution
                    fit.  Required with 'pdf', 'logpdf', or 'nloglf'.
                    
     'lowerbound'   A scalar or vector of lower bounds for the custom-distribution
                    parameters.  By default they are unbounded below.
                    
     'upperbound'   A scalar or vector of upper bounds for the custom-distribution
                    parameters.  By default they are unbounded above.
                    
     'truncationbounds'A two-element vector [L U] giving the truncation interval of a
                    custom distribution.  Requires a 'cdf' function.
                    
     'optimfun'     The optimizer for a custom-distribution fit.  Only
                    'fminsearch' is supported; bounded fits are handled by
                    internal reparameterization of the constrained parameters.

     When a custom distribution is specified through 'pdf', 'logpdf', or
     'nloglf', the parameters are estimated by maximizing the likelihood with
     ‘fminsearch’, and the second output PCI gives asymptotic normal (Wald)
     confidence intervals computed from the observed Fisher information at PHAT
     (see ‘mlecov’).  Bounded parameters are estimated on an internally
     reparameterized unconstrained scale.

     Distribution names are matched ignoring case, spaces and hyphens, so that
     'Extreme Value', 'ExtremeValue' and 'extreme-value' all select the same
     distribution, and the same set of names is accepted by ‘cdf’, ‘pdf’,
     ‘icdf’, ‘random’, ‘makedist’, ‘fitdist’ and ‘mle’.

     This accepts more names than MATLAB. MATLAB takes the spaced and the
     squashed spelling but refuses the hyphenated one, so 'Birnbaum-Saunders'
     and 'Log-Logistic' are errors there; Octave has always accepted them and
     continues to.  MATLAB also accepts 'tLocationScale' in ‘makedist’ while
     refusing it in ‘cdf’ for the same distribution; Octave accepts it, and
     'location-scale T', everywhere.  Code written against MATLAB's names
     therefore runs unchanged, but code relying on these names will not port
     back.

     See also: mlecov, fitdist, makedist.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 37
Compute maximum likelihood estimates.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
mlecov


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4710
 -- statistics: ACOV = mlecov (PARAMS, DATA, NAME, VALUE)

     Asymptotic covariance matrix of maximum likelihood estimators.

     ‘ACOV = mlecov (PARAMS, DATA, ...)’ returns an approximation to the
     asymptotic covariance matrix of the maximum likelihood estimators of the
     parameters of a distribution, evaluated at the parameter values in PARAMS
     for the sample data in DATA.  PARAMS is a numeric vector of parameter
     values (typically the estimates returned by ‘mle’ or ‘fitdist’) and DATA is
     a numeric vector of the sample observations.  ACOV is a p*p matrix, where p
     = numel (PARAMS).

     The distribution is not identified by name; instead it is supplied through
     Name-Value paired arguments that give function handles to its density, its
     log density, or its negative log-likelihood.  Exactly *one* of the
     following three arguments must be specified:

     NAME           VALUE
                    
     --------------------------------------------------------------------------------
     'pdf'          A function handle, ‘F(DATA, P1, P2, ...)’, that accepts the
                    sample data as its first argument and the distribution
                    parameters as subsequent scalar arguments, and returns a
                    vector of probability density values, one per observation.
                    
     'logpdf'       A function handle, ‘F(DATA, P1, P2, ...)’, with the same
                    calling convention as 'pdf' but returning the _logarithm_ of
                    the density.
                    
     'nloglf'       A function handle, ‘NLL(PARAMS, DATA, CENS, FREQ)’, that
                    returns the scalar negative log-likelihood of the whole
                    sample.  It receives the current parameter vector, the data,
                    the censoring vector, and the frequency vector, and is
                    responsible for incorporating censoring and frequency itself.
                    
     'cdf'          A function handle to the cumulative distribution function,
                    with the same calling convention as 'pdf'.  It is *required*
                    together with 'pdf' when the data are censored, so that
                    censored observations can contribute their survival
                    probability.
                    
     'logsf'        A function handle to the logarithm of the survivor function
                    log (1 - cdf), with the same calling convention as 'pdf'.  It
                    is *required* together with 'logpdf' when the data are
                    censored.
                    
     'Censoring'    A vector of the same size as DATA indicating censored
                    observations (nonzero for right-censored).  By default no
                    observation is censored.
                    
     'Frequency'    A vector of nonnegative integer counts of the same size as
                    DATA, giving the number of times each observation was
                    observed.  By default it is ones (size (DATA)).
                    
     'Options'      A structure that may contain a 'DerivStep' field specifying
                    the relative finite-difference step used to approximate the
                    Hessian (a positive scalar or a vector the same size as
                    PARAMS).  The default step is eps ^ (1/4).

     *Computation and numerical behavior.*  ‘mlecov’ approximates the covariance
     matrix as the inverse of the observed Fisher information, that is, the
     inverse of the Hessian of the _aggregate_ negative log-likelihood of the
     sample, evaluated by central finite differences at PARAMS.  The covariance
     is computed _at_ the supplied PARAMS; ‘mlecov’ does not refit the
     parameters, so PARAMS should be the maximum likelihood estimates for the
     result to be meaningful.

     Whichever of 'pdf', 'logpdf', or 'nloglf' is supplied, the Hessian is
     always formed by differencing the same aggregate negative log-likelihood
     rather than by differentiating the density itself.  This makes the three
     input forms consistent with one another and is numerically far more stable
     than differentiating a density; as a consequence ACOV may differ from other
     implementations (including MATLAB) in ill-conditioned cases where those
     differentiate the density directly and return unreliable values or ‘NaN’.
     If the computed Hessian is not positive definite (for example when PARAMS
     is not at a likelihood maximum), a warning is issued and ACOV is returned
     as an all-‘NaN’ matrix.

     See also: mle, fitdist, makedist.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 62
Asymptotic covariance matrix of maximum likelihood estimators.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3
pdf


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4759
 -- statistics: Y = pdf (NAME, X, A)
 -- statistics: Y = pdf (NAME, X, A, B)
 -- statistics: Y = pdf (NAME, X, A, B, C)

     Return the PDF of a univariate distribution evaluated at X.

     ‘pdf’ is a wrapper for the univariate cumulative distribution functions
     available in the statistics package.  See the corresponding functions' help
     to learn the signification of the parameters after X.

     ‘Y = pdf (NAME, X, A)’ returns the CDF for the one-parameter distribution
     family specified by NAME and the distribution parameter A, evaluated at the
     values in X.

     ‘Y = pdf (NAME, X, A, B)’ returns the CDF for the two-parameter
     distribution family specified by NAME and the distribution parameters A and
     B, evaluated at the values in X.

     ‘Y = pdf (NAME, X, A, B, C)’ returns the CDF for the three-parameter
     distribution family specified by NAME and the distribution parameters A, B,
     and C, evaluated at the values in X.

     NAME must be a char string of the name or the abbreviation of the desired
     cumulative distribution function as listed in the following table.  The
     last column shows the number of required parameters that should be parsed
     after X to the desired PDF.

     Distribution Name                Abbreviation     Input Parameters
     ---------------------------------------------------------------------------
     'Beta'                           'beta'           2
     'Binomial'                       'bino'           2
     'Birnbaum-Saunders'              'bisa'           2
     'Burr'                           'burr'           3
     'Cauchy'                         'cauchy'         2
     'Chi-squared'                    'chi2'           1
     'Extreme Value'                  'ev'             2
     'Exponential'                    'exp'            1
     'F-Distribution'                 'f'              2
     'Gamma'                          'gam'            2
     'Geometric'                      'geo'            1
     'Generalized Extreme Value'      'gev'            3
     'Generalized Pareto'             'gp'             3
     'Gumbel'                         'gumbel'         2
     'Half-normal'                    'hn'             2
     'Hypergeometric'                 'hyge'           3
     'Inverse Gaussian'               'invg'           2
     'Laplace'                        'laplace'        2
     'Logistic'                       'logi'           2
     'Log-Logistic'                   'logl'           2
     'Lognormal'                      'logn'           2
     'Nakagami'                       'naka'           2
     'Negative Binomial'              'nbin'           2
     'Noncentral F-Distribution'      'ncf'            3
     'Noncentral Student T'           'nct'            2
     'Noncentral Chi-Squared'         'ncx2'           2
     'Normal'                         'norm'           2
     'Poisson'                        'poiss'          1
     'Rayleigh'                       'rayl'           1
     'Rician'                         'rice'           2
     'Student T'                      't'              1
     'location-scale T'               'tls'            3
     'Triangular'                     'tri'            3
     'Discrete Uniform'               'unid'           1
     'Uniform'                        'unif'           2
     'Von Mises'                      'vm'             2
     'Weibull'                        'wbl'            2

     Distribution names are matched ignoring case, spaces and hyphens, so that
     'Extreme Value', 'ExtremeValue' and 'extreme-value' all select the same
     distribution, and the same set of names is accepted by ‘cdf’, ‘pdf’,
     ‘icdf’, ‘random’, ‘makedist’, ‘fitdist’ and ‘mle’.

     This accepts more names than MATLAB. MATLAB takes the spaced and the
     squashed spelling but refuses the hyphenated one, so 'Birnbaum-Saunders'
     and 'Log-Logistic' are errors there; Octave has always accepted them and
     continues to.  MATLAB also accepts 'tLocationScale' in ‘makedist’ while
     refusing it in ‘cdf’ for the same distribution; Octave accepts it, and
     'location-scale T', everywhere.  Code written against MATLAB's names
     therefore runs unchanged, but code relying on these names will not port
     back.

     See also: cdf, icdf, random, betapdf, binopdf, bisapdf, burrpdf, cauchypdf,
     chi2pdf, evpdf, exppdf, fpdf, gampdf, geopdf, gevpdf, gppdf, gumbelpdf,
     hnpdf, hygepdf, invgpdf, laplacepdf, logipdf, loglpdf, lognpdf, nakapdf,
     nbinpdf, ncfpdf, nctpdf, ncx2pdf, normpdf, poisspdf, raylpdf, ricepdf,
     tpdf, tlspdf, tripdf, unidpdf, unifpdf, vmpdf, wblpdf.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 59
Return the PDF of a univariate distribution evaluated at X.



# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
random


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4915
 -- statistics: R = random (NAME, A)
 -- statistics: R = random (NAME, A, B)
 -- statistics: R = random (NAME, A, B, C)
 -- statistics: R = random (NAME, ..., ROWS, COLS)
 -- statistics: R = random (NAME, ..., ROWS, COLS, ...)
 -- statistics: R = random (NAME, ..., [SZ])

     Random arrays from a given one-, two-, or three-parameter distribution.

     The variable NAME must be a string with the name of the distribution to
     sample from.  If this distribution is a one-parameter distribution, A must
     be supplied, if it is a two-parameter distribution, B must also be
     supplied, and if it is a three-parameter distribution, C must also be
     supplied.  Any arguments following the distribution parameters will
     determine the size of the result.

     When called with a single size argument, return 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 vector of dimensions SZ.

     NAME must be a char string of the name or the abbreviation of the desired
     probability distribution function as listed in the following table.  The
     last column shows the required number of parameters that must be passed to
     the desired *rnd distribution function.

     Distribution Name                Abbreviation     Input Parameters
     ---------------------------------------------------------------------------
     'Beta'                           'beta'           2
     'Binomial'                       'bino'           2
     'Birnbaum-Saunders'              'bisa'           2
     'Burr'                           'burr'           3
     'Cauchy'                         'cauchy'         2
     'Chi-squared'                    'chi2'           1
     'Extreme Value'                  'ev'             2
     'Exponential'                    'exp'            1
     'F-Distribution'                 'f'              2
     'Gamma'                          'gam'            2
     'Geometric'                      'geo'            1
     'Generalized Extreme Value'      'gev'            3
     'Generalized Pareto'             'gp'             3
     'Gumbel'                         'gumbel'         2
     'Half-normal'                    'hn'             2
     'Hypergeometric'                 'hyge'           3
     'Inverse Gaussian'               'invg'           2
     'Laplace'                        'laplace'        2
     'Logistic'                       'logi'           2
     'Log-Logistic'                   'logl'           2
     'Lognormal'                      'logn'           2
     'Nakagami'                       'naka'           2
     'Negative Binomial'              'nbin'           2
     'Noncentral F-Distribution'      'ncf'            3
     'Noncentral Student T'           'nct'            2
     'Noncentral Chi-Squared'         'ncx2'           2
     'Normal'                         'norm'           2
     'Poisson'                        'poiss'          1
     'Rayleigh'                       'rayl'           1
     'Rician'                         'rice'           2
     'Student T'                      't'              1
     'location-scale T'               'tls'            3
     'Triangular'                     'tri'            3
     'Discrete Uniform'               'unid'           1
     'Uniform'                        'unif'           2
     'Von Mises'                      'vm'             2
     'Weibull'                        'wbl'            2

     Distribution names are matched ignoring case, spaces and hyphens, so that
     'Extreme Value', 'ExtremeValue' and 'extreme-value' all select the same
     distribution, and the same set of names is accepted by ‘cdf’, ‘pdf’,
     ‘icdf’, ‘random’, ‘makedist’, ‘fitdist’ and ‘mle’.

     This accepts more names than MATLAB. MATLAB takes the spaced and the
     squashed spelling but refuses the hyphenated one, so 'Birnbaum-Saunders'
     and 'Log-Logistic' are errors there; Octave has always accepted them and
     continues to.  MATLAB also accepts 'tLocationScale' in ‘makedist’ while
     refusing it in ‘cdf’ for the same distribution; Octave accepts it, and
     'location-scale T', everywhere.  Code written against MATLAB's names
     therefore runs unchanged, but code relying on these names will not port
     back.

     See also: cdf, icdf, pdf, betarnd, binornd, bisarnd, burrrnd, cauchyrnd,
     chi2rnd, evrnd, exprnd, frnd, gamrnd, geornd, gevrnd, gprnd, gumbelrnd,
     hnrnd, hygernd, invgrnd, laplacernd, logirnd, loglrnd, lognrnd, nakarnd,
     nbinrnd, ncfrnd, nctrnd, ncx2rnd, normrnd, poissrnd, raylrnd, ricernd,
     trnd, tlsrnd, trirnd, unidrnd, unifrnd, vmrnd, wblrnd.


# name: <cell-element>
# type: sq_string
# elements: 1
# length: 71
Random arrays from a given one-, two-, or three-parameter distribution.





