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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.





