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- /* randist/poisson.c
- *
- * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 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 3 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 "gsl__config.h"
- #include <math.h>
- #include "gsl_sf_gamma.h"
- #include "gsl_rng.h"
- #include "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;
- }
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