/* cdf/hypergeometric.c

 *

 * Copyright (C) 2004 Jason H. Stover.

 *

 * 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.

 */

/*

 * Computes the cumulative distribution function for a hypergeometric

 * random variable. A hypergeometric random variable X is the number

 * of elements of type 1 in a sample of size t, drawn from a population

 * of size n1 + n2, in which n1 are of type 1 and n2 are of type 2.

 *

 * This algorithm computes Pr( X <= k ) by summing the terms from

 * the mass function, Pr( X = k ).

 *

 * References:

 *

 * T. Wu. An accurate computation of the hypergeometric distribution 

 * function. ACM Transactions on Mathematical Software. Volume 19, number 1,

 * March 1993.

 *  This algorithm is not used, since it requires factoring the

 *  numerator and denominator, then cancelling. It is more accurate

 *  than the algorithm used here, but the cancellation requires more

 *  time than the algorithm used here.

 *

 * W. Feller. An Introduction to Probability Theory and Its Applications,

 * third edition. 1968. Chapter 2, section 6. 

 */

#include <config.h>

#include <math.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_errno.h>

#include <gsl/gsl_cdf.h>

#include <gsl/gsl_randist.h>

#include "error.h"

static double

lower_tail (const unsigned int k, const unsigned int n1,

            const unsigned int n2, const unsigned int t)

{

  double relerr;

  int i = k;

  double s, P;

  s = gsl_ran_hypergeometric_pdf (i, n1, n2, t);

  P = s;

  while (i > 0)

    {

      double factor =

        (i / (n1 - i + 1.0)) * ((n2 + i - t) / (t - i + 1.0));

      s *= factor;

      P += s;

      relerr = s / P;

      if (relerr < GSL_DBL_EPSILON)

        break;

      i--;

    }

  return P;

}

static double 

upper_tail (const unsigned int k, const unsigned int n1,

            const unsigned int n2, const unsigned int t)

{

  double relerr;

  unsigned int i = k + 1;

  double s, Q;

  s = gsl_ran_hypergeometric_pdf (i, n1, n2, t);

  Q = s;

  while (i < t)

    {

      double factor =

        ((n1 - i) / (i + 1.0)) * ((t - i) / (n2 + i + 1.0 - t));

      s *= factor;

      Q += s;

      relerr = s / Q;

      if (relerr < GSL_DBL_EPSILON)

        break;

      i++;

    }

  return Q;

}

/*

 * Pr (X <= k)

 */

double

gsl_cdf_hypergeometric_P (const unsigned int k,

                          const unsigned int n1,

                          const unsigned int n2, const unsigned int t)

{

  double P;

  if (t > (n1 + n2))

    {

      CDF_ERROR ("t larger than population size", GSL_EDOM);

    }

  else if (k >= n1 || k >= t)

    {

      P = 1.0;

    }

  else if (k < 0.0)

    {

      P = 0.0;

    }

  else

    {

      double midpoint = ((double)t * n1) / ((double)n1 + (double)n2);

      if (k >= midpoint)

        {

          P = 1 - upper_tail (k, n1, n2, t);

        }

      else

        {

          P = lower_tail (k, n1, n2, t);

        }

    }

  return P;

}

/*

 * Pr (X > k)

 */

double

gsl_cdf_hypergeometric_Q (const unsigned int k,

                          const unsigned int n1,

                          const unsigned int n2, const unsigned int t)

{

  double Q;

  if (t > (n1 + n2))

    {

      CDF_ERROR ("t larger than population size", GSL_EDOM);

    }

  else if (k >= n1 || k >= t)

    {

      Q = 0.0;

    }

  else if (k < 0.0)

    {

      Q = 1.0;

    }

  else

    {

      double midpoint = ((double)t * n1) / ((double)n1 + (double)n2);

      if (k < midpoint)

        {

          Q = 1 - lower_tail (k, n1, n2, t);

        }

      else

        {

          Q = upper_tail (k, n1, n2, t);

        }

    }

  return Q;

}