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- /* randist/binomial.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_sys.h"
- #include "gsl_rng.h"
- #include "gsl_randist.h"
- #include "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;
- }
- }
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