/* 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; }