/* cdf/poisson.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 Poisson

 * random variable. For a Poisson random variable X with parameter

 * mu,

 *

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

 *

 * where Y is a gamma random variable with parameters k+1 and 1.

 *

 * Reference: 

 * 

 * W. Feller, "An Introduction to Probability and Its

 * Applications," volume 1. Wiley, 1968. Exercise 46, 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>

#include "error.h"

/*

 * Pr (X <= k) for a Poisson random variable X.

 */

double

gsl_cdf_poisson_P (const unsigned int k, const double mu)

{

  double P;

  double a;

  if (mu <= 0.0)

    {

      CDF_ERROR ("mu <= 0", GSL_EDOM);

    }

  a = (double) k + 1.0;

  P = gsl_cdf_gamma_Q (mu, a, 1.0);

  return P;

}

/*

 * Pr ( X > k ) for a Possion random variable X.

 */

double

gsl_cdf_poisson_Q (const unsigned int k, const double mu)

{

  double Q;

  double a;

  if (mu <= 0.0)

    {

      CDF_ERROR ("mu <= 0", GSL_EDOM);

    }

  a = (double) k + 1.0;

  Q = gsl_cdf_gamma_P (mu, a, 1.0);

  return Q;

}