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cdf


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 -- 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

     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.


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Return the CDF of a univariate distribution evaluated at X.



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fitdist


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 -- 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.
                       
     "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.

     See also: makedist.


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Create probability distribution object.



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icdf


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 -- 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

     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.


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



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makedist


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 -- 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.

     See also: fitdist.


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Create probability distribution object.



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mle


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 -- 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.
                       
     "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.

     See also: fitdist, makedist.


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Compute maximum likelihood estimates.



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pdf


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 -- 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

     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.


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Return the PDF of a univariate distribution evaluated at X.



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random


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 -- 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

     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.


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





