Statistics::GammaDistribution - represents a gamma distribution
use Statistics::GammaDistribution; my $g = Statistics::GammaDistribution->new(); $g->set_order(8.5); print $g->rand(1.0); my @alpha = (0.5,4.5,20.5,6.5,1.5,0.5); my @theta = $g->dirichlet_dist(@alpha);
No parameters necessary.
This function returns a random variate from the gamma distribution. The distribution function is,
p(x) dx = {1 \over \Gamma(a) b^a} x^{a-1} e^{-x/b} dx
for x > 0.
Where a is the order and b is the scale. Unless supplied as a parameter, SCALE is assumed to be 1.0 if not supplied.
Gets/sets the order of the distribution. Order must be greater than zero.
Takes a K-sized array of real numbers (all greater than zero), and returns a K-sized array containing random variates from a Dirichlet distribution. The distribution function is
p(\theta_1, ..., \theta_K) d\theta_1 ... d\theta_K =
(1/Z) \prod_{i=1}^K \theta_i^{\alpha_i - 1} \delta(1 -\sum_{i=1}^K \theta_i) d\theta_1 ... d\theta_K
for theta_i >= 0 and alpha_i >= 0. The normalization factor Z is
Z = {\prod_{i=1}^K \Gamma(\alpha_i)} / {\Gamma( \sum_{i=1}^K \alpha_i)}
The random variates are generated by sampling K values from gamma distributions with parameters order=alpha_i, scale=1, and renormalizing. See A.M. Law, W.D. Kelton, Simulation Modeling and Analysis (1991).
Nigel Wetters Gourlay <nwetters@cpan.org>
Copyright (c) 2003-06, Nigel Wetters Gourlay. NO WARRANTY.
This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.
