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/* randist/binomial.c
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 James Theiler, Brian Gough
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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#include <config.h>
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#include <math.h>
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#include <gsl/gsl_sys.h>
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#include <gsl/gsl_rng.h>
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#include <gsl/gsl_randist.h>
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#include <gsl/gsl_sf_gamma.h>
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/* The binomial distribution has the form,
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prob(k) = n!/(k!(n-k)!) * p^k (1-p)^(n-k) for k = 0, 1, ..., n
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This is the algorithm from Knuth */
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/* Default binomial generator is now in binomial_tpe.c */
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unsigned int
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gsl_ran_binomial_knuth (const gsl_rng * r, double p, unsigned int n)
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{
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unsigned int i, a, b, k = 0;
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while (n > 10) /* This parameter is tunable */
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{
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double X;
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a = 1 + (n / 2);
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b = 1 + n - a;
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X = gsl_ran_beta (r, (double) a, (double) b);
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if (X >= p)
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{
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n = a - 1;
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p /= X;
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}
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else
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{
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k += a;
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n = b - 1;
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p = (p - X) / (1 - X);
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}
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}
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for (i = 0; i < n; i++)
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{
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double u = gsl_rng_uniform (r);
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if (u < p)
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k++;
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}
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return k;
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}
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double
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gsl_ran_binomial_pdf (const unsigned int k, const double p,
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const unsigned int n)
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{
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if (k > n)
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{
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return 0;
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}
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else
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{
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double P;
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if (p == 0)
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{
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P = (k == 0) ? 1 : 0;
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}
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else if (p == 1)
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{
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P = (k == n) ? 1 : 0;
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}
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else
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{
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double ln_Cnk = gsl_sf_lnchoose (n, k);
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P = ln_Cnk + k * log (p) + (n - k) * log1p (-p);
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P = exp (P);
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}
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return P;
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}
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}
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