Module Version: 0.02

# NAME

Statistics::GammaDistribution - 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) 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).

# AUTHOR

Nigel Wetters Gourlay <nwetters@cpan.org>