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/* randist/poisson.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_sf_gamma.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
/* The poisson distribution has the form
p(n) = (mu^n / n!) exp(-mu)
for n = 0, 1, 2, ... . The method used here is the one from Knuth. */
unsigned int
gsl_ran_poisson (const gsl_rng * r, double mu)
{
double emu;
double prod = 1.0;
unsigned int k = 0;
while (mu > 10)
{
unsigned int m = mu * (7.0 / 8.0);
double X = gsl_ran_gamma_int (r, m);
if (X >= mu)
{
return k + gsl_ran_binomial (r, mu / X, m - 1);
}
else
{
k += m;
mu -= X;
}
}
/* This following method works well when mu is small */
emu = exp (-mu);
do
{
prod *= gsl_rng_uniform (r);
k++;
}
while (prod > emu);
return k - 1;
}
void
gsl_ran_poisson_array (const gsl_rng * r, size_t n, unsigned int array[],
double mu)
{
size_t i;
for (i = 0; i < n; i++)
{
array[i] = gsl_ran_poisson (r, mu);
}
return;
}
double
gsl_ran_poisson_pdf (const unsigned int k, const double mu)
{
double p;
double lf = gsl_sf_lnfact (k);
p = exp (log (mu) * k - lf - mu);
return p;
}
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