| /* 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 |
| * 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; |
| } |