# FreeBSD Manual Pages

```Math::GSL::CDF(3)     User Contributed Perl Documentation    Math::GSL::CDF(3)

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	informations on	the functions, we refer	you to the GSL offcial
documentation: <http://www.gnu.org/software/gsl/manual/html_node/>

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