| /* randist/nbinomial.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_rng.h> |
| #include <gsl/gsl_randist.h> |
| #include <gsl/gsl_sf_gamma.h> |
| |
| /* The negative binomial distribution has the form, |
| |
| prob(k) = Gamma(n + k)/(Gamma(n) Gamma(k + 1)) p^n (1-p)^k |
| |
| for k = 0, 1, ... . Note that n does not have to be an integer. |
| |
| This is the Leger's algorithm (given in the answers in Knuth) */ |
| |
| unsigned int |
| gsl_ran_negative_binomial (const gsl_rng * r, double p, double n) |
| { |
| double X = gsl_ran_gamma (r, n, 1.0) ; |
| unsigned int k = gsl_ran_poisson (r, X*(1-p)/p) ; |
| return k ; |
| } |
| |
| double |
| gsl_ran_negative_binomial_pdf (const unsigned int k, const double p, double n) |
| { |
| double P; |
| |
| double f = gsl_sf_lngamma (k + n) ; |
| double a = gsl_sf_lngamma (n) ; |
| double b = gsl_sf_lngamma (k + 1.0) ; |
| |
| P = exp(f-a-b) * pow (p, n) * pow (1 - p, (double)k); |
| |
| return P; |
| } |