NAME

PDL::GSL::CDF - PDL interface to GSL Cumulative Distribution Functions

DESCRIPTION

This is an interface to the Cumulative Distribution Function package present in the GNU Scientific Library.

Let us have a continuous random number distributions are defined by a probability density function p(x).

The cumulative distribution function for the lower tail P(x) is defined by the integral of p(x), and gives the probability of a variate taking a value less than x. These functions are named cdf_NNNNNNN_P().

The cumulative distribution function for the upper tail Q(x) is defined by the integral of p(x), and gives the probability of a variate taking a value greater than x. These functions are named cdf_NNNNNNN_Q().

The upper and lower cumulative distribution functions are related by P(x) + Q(x) = 1 and satisfy 0 <= P(x) <= 1 and 0 <= Q(x) <= 1.

The inverse cumulative distributions, x = Pinv(P) and x = Qinv(Q) give the values of x which correspond to a specific value of P or Q. They can be used to find confidence limits from probability values. These functions are named cdf_NNNNNNN_Pinv() and cdf_NNNNNNN_Qinv().

For discrete distributions the probability of sampling the integer value k is given by p(k), where sum_k p(k) = 1. The cumulative distribution for the lower tail P(k) of a discrete distribution is defined as, where the sum is over the allowed range of the distribution less than or equal to k.

The cumulative distribution for the upper tail of a discrete distribution Q(k) is defined as giving the sum of probabilities for all values greater than k. These two definitions satisfy the identity P(k) + Q(k) = 1.

If the range of the distribution is 1 to n inclusive then P(n) = 1, Q(n) = 0 while P(1) = p(1), Q(1) = 1 - p(1).

SYNOPSIS

use PDL;
use PDL::GSL::CDF;

my $p = gsl_cdf_tdist_P( $t, $df );

my $t = gsl_cdf_tdist_Pinv( $p, $df );

AUTHOR

Copyright (C) 2009 Maggie J. Xiong <maggiexyz users.sourceforge.net>

The GSL CDF module was written by J. Stover.

All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation as described in the file COPYING in the PDL distribution.