| /* randist/binomial.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_sys.h> |
| #include <gsl/gsl_rng.h> |
| #include <gsl/gsl_randist.h> |
| #include <gsl/gsl_sf_gamma.h> |
| |
| /* The binomial distribution has the form, |
| |
| prob(k) = n!/(k!(n-k)!) * p^k (1-p)^(n-k) for k = 0, 1, ..., n |
| |
| This is the algorithm from Knuth */ |
| |
| /* Default binomial generator is now in binomial_tpe.c */ |
| |
| unsigned int |
| gsl_ran_binomial_knuth (const gsl_rng * r, double p, unsigned int n) |
| { |
| unsigned int i, a, b, k = 0; |
| |
| while (n > 10) /* This parameter is tunable */ |
| { |
| double X; |
| a = 1 + (n / 2); |
| b = 1 + n - a; |
| |
| X = gsl_ran_beta (r, (double) a, (double) b); |
| |
| if (X >= p) |
| { |
| n = a - 1; |
| p /= X; |
| } |
| else |
| { |
| k += a; |
| n = b - 1; |
| p = (p - X) / (1 - X); |
| } |
| } |
| |
| for (i = 0; i < n; i++) |
| { |
| double u = gsl_rng_uniform (r); |
| if (u < p) |
| k++; |
| } |
| |
| return k; |
| } |
| |
| double |
| gsl_ran_binomial_pdf (const unsigned int k, const double p, |
| const unsigned int n) |
| { |
| if (k > n) |
| { |
| return 0; |
| } |
| else |
| { |
| double P; |
| |
| if (p == 0) |
| { |
| P = (k == 0) ? 1 : 0; |
| } |
| else if (p == 1) |
| { |
| P = (k == n) ? 1 : 0; |
| } |
| else |
| { |
| double ln_Cnk = gsl_sf_lnchoose (n, k); |
| P = ln_Cnk + k * log (p) + (n - k) * log1p (-p); |
| P = exp (P); |
| } |
| |
| return P; |
| } |
| } |