---
name: "Math::GSL::CDF"
section: "3pm"
platform: "linux"
package: "libmath-gsl-perl"
version: "0.45-2+b1"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/Math::GSL::CDF"
---

# Math::GSL::CDF(3pm)

Cumulative Distribution Functions

## 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) 2008-2024 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.