/* 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 <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;

    }

}