/* 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 2 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
*/
/*
* Computes the cumulative distribution function for a Poisson
* random variable. For a Poisson random variable X with parameter
* lambda,
*
* 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
#include
#include
#include
#include
/*
* Pr (X <= k) for a Poisson random variable X.
*/
double
gsl_cdf_poisson_P (const long k, const double lambda)
{
double P;
double a;
if ( lambda <= 0.0 )
{
GSL_CDF_ERROR ("lambda <= 0", GSL_EDOM);
}
if ( k < 0 )
{
P = 0.0;
}
else
{
a = (double) k+1;
P = gsl_cdf_gamma_Q ( lambda, a, 1.0);
}
return P;
}
/*
* Pr ( X > k ) for a Possion random variable X.
*/
double
gsl_cdf_poisson_Q (const long k, const double lambda)
{
double P;
double a;
if ( lambda <= 0.0 )
{
GSL_CDF_ERROR ("lambda <= 0", GSL_EDOM);
}
if ( k < 0 )
{
P = 1.0;
}
else
{
a = (double) k+1;
P = gsl_cdf_gamma_P ( lambda, a, 1.0);
}
return P;
}