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Date Added: March 26, 2010  |  Visits: 624

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)..

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