Statistics::GammaDistribution 0.02

Statistics::GammaDistribution Perl module represents a gamma distribution.

SYNOPSIS

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);

METHODS

$gamma = Statistics::GammaDistribution->new();

No parameters necessary.

$variate = $gamma->rand( SCALE );

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.
$gamma->get/set_order( ORDER );

Gets/sets the order of the distribution. Order must be greater than zero.

@theta = $gamma->dirichlet_dist( ALPHA );

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) dtheta_1 ... dtheta_K =
(1/Z) prod_{i=1}^K theta_i^{alpha_i - 1} delta(1 -sum_{i=1}^K theta_i) dtheta_1 ... dtheta_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).