| /* randist/poisson.c |
| * |
| * Copyright (C) 1996, 1997, 1998, 1999, 2000 James Theiler, Brian Gough |
| * |
| * 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. |
| * |
| * This program is distributed in the hope that it will be useful, but |
| * WITHOUT ANY WARRANTY; without even the implied warranty of |
| * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| * General Public License for more details. |
| * |
| * You should have received a copy of the GNU General Public License |
| * along with this program; if not, write to the Free Software |
| * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. |
| */ |
| |
| #include <config.h> |
| #include <math.h> |
| #include <gsl/gsl_sf_gamma.h> |
| #include <gsl/gsl_rng.h> |
| #include <gsl/gsl_randist.h> |
| |
| /* The poisson distribution has the form |
| |
| p(n) = (mu^n / n!) exp(-mu) |
| |
| for n = 0, 1, 2, ... . The method used here is the one from Knuth. */ |
| |
| unsigned int |
| gsl_ran_poisson (const gsl_rng * r, double mu) |
| { |
| double emu; |
| double prod = 1.0; |
| unsigned int k = 0; |
| |
| while (mu > 10) |
| { |
| unsigned int m = mu * (7.0 / 8.0); |
| |
| double X = gsl_ran_gamma_int (r, m); |
| |
| if (X >= mu) |
| { |
| return k + gsl_ran_binomial (r, mu / X, m - 1); |
| } |
| else |
| { |
| k += m; |
| mu -= X; |
| } |
| } |
| |
| /* This following method works well when mu is small */ |
| |
| emu = exp (-mu); |
| |
| do |
| { |
| prod *= gsl_rng_uniform (r); |
| k++; |
| } |
| while (prod > emu); |
| |
| return k - 1; |
| |
| } |
| |
| void |
| gsl_ran_poisson_array (const gsl_rng * r, size_t n, unsigned int array[], |
| double mu) |
| { |
| size_t i; |
| |
| for (i = 0; i < n; i++) |
| { |
| array[i] = gsl_ran_poisson (r, mu); |
| } |
| |
| return; |
| } |
| |
| double |
| gsl_ran_poisson_pdf (const unsigned int k, const double mu) |
| { |
| double p; |
| double lf = gsl_sf_lnfact (k); |
| |
| p = exp (log (mu) * k - lf - mu); |
| return p; |
| } |