text: /* 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;
      }
  }
  