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/* randist/nbinomial.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 <config.h>
#include <math.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
#include <gsl/gsl_sf_gamma.h>
#include <gsl/gsl_sys.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 + n * log(p) + k * log1p(-p));
return P;
}
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