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# 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> Visit the GSP FreeBSD Man Page Interface.