/* cdf/binomial.c

 * 

 * Copyright (C) 2004 Jason H. Stover.

 * Copyright (C) 2004 Giulio Bottazzi

 * 

 * 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., 675 Mass Ave, Cambridge, MA 02139, USA.

 */

#include <config.h>

#include <math.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_cdf.h>

#include <gsl/gsl_sf_gamma.h>

#include "error.h"

/* Computes the cumulative distribution function for a binomial

   random variable. For a binomial random variable X with n trials

   and success probability p,

           Pr( X <= k ) = Pr( Y >= p )

   where Y is a beta random variable with parameters k+1 and n-k.

   The binomial distribution has the form,

   prob(k) =  n!/(k!(n-k)!) *  p^k (1-p)^(n-k) for k = 0, 1, ..., n

   The cumulated distributions can be expressed in terms of normalized

   incomplete beta functions (see Abramowitz & Stegun eq. 26.5.26 and

   eq. 6.6.3).

   Reference: 

   W. Feller, "An Introduction to Probability and Its

   Applications," volume 1. Wiley, 1968. Exercise 45, page 173,

   chapter 6.

 */

#include <config.h>

#include <math.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_errno.h>

#include <gsl/gsl_cdf.h>

double

gsl_cdf_binomial_P (const unsigned int k, const double p, const unsigned int n)

{

  double P;

  double a;

  double b;

  if (p > 1.0 || p < 0.0)

    {

      CDF_ERROR ("p < 0 or p > 1", GSL_EDOM);

    }

  if (k >= n)

    {

      P = 1.0;

    }

  else

    {

      a = (double) k + 1.0;

      b = (double) n - k;

      P = gsl_cdf_beta_Q (p, a, b);

    }

  return P;

}

double

gsl_cdf_binomial_Q (const unsigned int k, const double p, const unsigned int n)

{

  double Q;

  double a;

  double b;

  if (p > 1.0 || p < 0.0)

    {

      CDF_ERROR ("p < 0 or p > 1", GSL_EDOM);

    }

  if (k >= n)

    {

      Q = 0.0;

    }

  else

    {

      a = (double) k + 1.0;

      b = (double) n - k;

      Q = gsl_cdf_beta_P (p, a, b);

    }

  return Q;

}