Provided by: libmath-gsl-perl_0.44-1build3_amd64 bug

NAME

       Math::GSL::CDF - Cumulative Distribution Functions

SYNOPSIS

           use Math::GSL::CDF qw/:all/;
           my $x = gsl_cdf_gaussian_Pinv($P, $sigma);

           use Math::GSL::CDF qw/:beta/;
           print gsl_cdf_beta_P(1,2,3) . "\n";

       These functions compute the cumulative distribution functions P(x), Q(x) and their
       inverses for the named distributions.

DESCRIPTION

       Here is a list of all the functions included in this module :

       gsl_cdf_ugaussian_P($x)
       gsl_cdf_ugaussian_Q($x)
       gsl_cdf_ugaussian_Pinv($P)
       gsl_cdf_ugaussian_Qinv($Q)
           These functions compute the cumulative distribution functions P(x), Q(x) and their
           inverses for the unit Gaussian distribution.

       gsl_cdf_gaussian_P($x, $sigma)
       gsl_cdf_gaussian_Q($x, $sigma)
       gsl_cdf_gaussian_Pinv($P, $sigma)
       gsl_cdf_gaussian_Qinv($Q, $sigma)
           These functions compute the cumulative distribution functions P(x), Q(x) and their
           inverses for the Gaussian distribution with standard deviation $sigma.

       gsl_cdf_gamma_P($x, $a, $b)
       gsl_cdf_gamma_Q($x, $a, $b)
       gsl_cdf_gamma_Pinv($P, $a, $b)
       gsl_cdf_gamma_Qinv($Q, $a, $b)
           These functions compute the cumulative distribution functions P(x), Q(x) and their
           inverses for the gamma distribution with parameters $a and $b.

       gsl_cdf_cauchy_P($x, $a)
       gsl_cdf_cauchy_Q($x, $a)
       gsl_cdf_cauchy_Pinv($P, $a)
       gsl_cdf_cauchy_Qinv($Q, $a)
           These functions compute the cumulative distribution functions P(x), Q(x) and their
           inverses for the Cauchy distribution with scale parameter $a.

       gsl_cdf_laplace_P($x, $a)
       gsl_cdf_laplace_Q($x, $a)
       gsl_cdf_laplace_Pinv($P, $a)
       gsl_cdf_laplace_Qinv($Q, $a)
           These functions compute the cumulative distribution functions P(x), Q(x) and their
           inverses for the Laplace distribution with width $a.

       gsl_cdf_rayleigh_P($x, $sigma)
       gsl_cdf_rayleigh_Q($x, $sigma)
       gsl_cdf_rayleigh_Pinv($P, $sigma)
       gsl_cdf_rayleigh_Qinv($Q, $sigma)
           These functions compute the cumulative distribution functions P(x), Q(x) and their
           inverses for the Rayleigh distribution with scale parameter $sigma.

       gsl_cdf_chisq_P($x, $nu)
       gsl_cdf_chisq_Q($x, $nu)
       gsl_cdf_chisq_Pinv($P, $nu)
       gsl_cdf_chisq_Qinv($Q, $nu)
           These functions compute the cumulative distribution functions P(x), Q(x) and their
           inverses for the chi-squared distribution with $nu degrees of freedom.

       gsl_cdf_exponential_P($x, $mu)
       gsl_cdf_exponential_Q($x, $mu)
       gsl_cdf_exponential_Pinv($P, $mu)
       gsl_cdf_exponential_Qinv($Q, $mu)
           These functions compute the cumulative distribution functions P(x), Q(x) and their
           inverses for the Laplace distribution with width $a.

       gsl_cdf_exppow_P($x, $a, $b)
       gsl_cdf_exppow_Q($x, $a, $b)
           These functions compute the cumulative distribution functions P(x), Q(x) for the
           exponential power distribution with parameters $a and $b.

       gsl_cdf_tdist_P($x, $nu)
       gsl_cdf_tdist_Q($x, $nu)
       gsl_cdf_tdist_Pinv($P, $nu)
       gsl_cdf_tdist_Qinv($Q, $nu)
           These functions compute the cumulative distribution functions P(x), Q(x) and their
           inverses for the t-distribution with $nu degrees of freedom.

       gsl_cdf_fdist_P($x, $nu1, $nu2)
       gsl_cdf_fdist_Q($x, $nu1, $nu2)
       gsl_cdf_fdist_Pinv($P, $nu1, $nu2)
       gsl_cdf_fdist_Qinv($Q, $nu1, $nu2)
           These functions compute the cumulative distribution functions P(x), Q(x) and their
           inverses for the F-distribution with $nu1 and $nu2 degrees of freedom.

       gsl_cdf_beta_P($x, $a, $b)
       gsl_cdf_beta_Q($x, $a, $b)
       gsl_cdf_beta_Pinv($P, $a, $b)
       gsl_cdf_beta_Qinv($Q, $a, $b)
           These functions compute the cumulative distribution functions P(x), Q(x) and their
           inverses for the beta distribution with parameters $a and $b.

       gsl_cdf_flat_P($x, $a, $b)
       gsl_cdf_flat_Q($x, $a, $b)
       gsl_cdf_flat_Pinv($P, $a, $b)
       gsl_cdf_flat_Qinv($Q, $a, $b)
           These functions compute the cumulative distribution functions P(x), Q(x) and their
           inverses for a uniform distribution from $a to $b.

       gsl_cdf_lognormal_P($x, $zeta, $sigma)
       gsl_cdf_lognormal_Q($x, $zeta, $sigma)
       gsl_cdf_lognormal_Pinv($P, $zeta, $sigma)
       gsl_cdf_lognormal_Qinv($Q, $zeta, $sigma)
           These functions compute the cumulative distribution functions P(x), Q(x) and their
           inverses for the lognormal distribution with parameters $zeta and $sigma.

       gsl_cdf_gumbel1_P($x, $a, $b)
       gsl_cdf_gumbel1_Q($x, $a, $b)
       gsl_cdf_gumbel1_Pinv($P, $a, $b)
       gsl_cdf_gumbel1_Qinv($Q, $a, $b)
           These functions compute the cumulative distribution functions P(x), Q(x) and their
           inverses for the Type-1 Gumbel distribution with parameters $a and $b.

       gsl_cdf_gumbel2_P($x, $a, $b)
       gsl_cdf_gumbel2_Q($x, $a, $b)
       gsl_cdf_gumbel2_Pinv($P, $a, $b)
       gsl_cdf_gumbel2_Qinv($Q, $a, $b)
           These functions compute the cumulative distribution functions P(x), Q(x) and their
           inverses for the Type-2 Gumbel distribution with parameters $a and $b.

       gsl_cdf_weibull_P($x, $a, $b)
       gsl_cdf_weibull_Q($x, $a, $b)
       gsl_cdf_weibull_Pinv($P, $a, $b)
       gsl_cdf_weibull_Qinv($Q, $a, $b)
           These functions compute the cumulative distribution functions P(x), Q(x) and their
           inverses for the Type-1 Gumbel distribution with parameters $a and $b.

       gsl_cdf_pareto_P($x, $a, $b)
       gsl_cdf_pareto_Q($x, $a, $b)
       gsl_cdf_pareto_Pinv($P, $a, $b)
       gsl_cdf_pareto_Qinv($Q, $a, $b)
           These functions compute the cumulative distribution functions P(x), Q(x) and their
           inverses for the Pareto distribution with exponent $a and scale $b.

       gsl_cdf_logistic_P($x, $a)
       gsl_cdf_logistic_Q($x, $a)
       gsl_cdf_logistic_Pinv($P, $a)
       gsl_cdf_logistic_Qinv($Q, $a)
           These functions compute the cumulative distribution functions P(x), Q(x) and their
           inverses for the logistic distribution with scale parameter a.

       gsl_cdf_binomial_P($k, $p, $n)
       gsl_cdf_binomial_Q($k, $p, $n)
           These functions compute the cumulative distribution functions P(k), Q(k) for the
           binomial distribution with parameters $p and $n.

       gsl_cdf_poisson_P($k, $mu)
       gsl_cdf_poisson_Q($k, $mu)
           These functions compute the cumulative distribution functions P(k), Q(k) for the
           Poisson distribution with parameter $mu.

       gsl_cdf_geometric_P($k, $p)
       gsl_cdf_geometric_Q($k, $p)
           These functions compute the cumulative distribution functions P(k), Q(k) for the
           geometric distribution with parameter $p.

       gsl_cdf_negative_binomial_P($k, $p, $n)
       gsl_cdf_negative_binomial_Q($k, $p, $n)
           These functions compute the cumulative distribution functions P(k), Q(k) for the
           negative binomial distribution with parameters $p and $n.

       gsl_cdf_pascal_P($k, $p, $n)
       gsl_cdf_pascal_Q($k, $p, $n)
           These functions compute the cumulative distribution functions P(k), Q(k) for the
           Pascal distribution with parameters $p and $n.

       gsl_cdf_hypergeometric_P($k, $n1, $n2, $t)
       gsl_cdf_hypergeometric_Q($k, $n1, $n2, $t)
           These functions compute the cumulative distribution functions P(k), Q(k) for the
           hypergeometric distribution with parameters $n1, $n2 and $t.

       To import specific functions, list them in the use line. To import all function exportable
       by Math::GSL::CDF do

           use Math::GSL::CDF qw/:all/

       This is the list of available import tags:

       geometric
       tdist
       ugaussian
       rayleigh
       pascal
       exponential
       gumbel2
       gumbel1
       exppow
       logistic
       weibull
       gaussian
       poisson
       beta
       binomial
       laplace
       lognormal
       cauchy
       fdist
       chisq
       gamma
       hypergeometric
       negative
       pareto
       flat

       For example the beta tag contains theses functions : gsl_cdf_beta_P, gsl_cdf_beta_Q,
       gsl_cdf_beta_Pinv, gsl_cdf_beta_Qinv .

       For more information on the functions, we refer you to the GSL official documentation:
       <http://www.gnu.org/software/gsl/manual/html_node/>

AUTHORS

       Jonathan "Duke" Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>

COPYRIGHT AND LICENSE

       Copyright (C) 2008-2023 Jonathan "Duke" Leto and Thierry Moisan

       This program is free software; you can redistribute it and/or modify it under the same
       terms as Perl itself.