/* cdf/binomial.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 binomial * random variable. For a binomial random variable X with n trials * and success probability p, * * Pr( X <= k ) = Pr( Y >= p ) * * where Y is a beta random variable with parameters k+1 and n-k. * * Reference: * * W. Feller, "An Introduction to Probability and Its * Applications," volume 1. Wiley, 1968. Exercise 45, page 173, * chapter 6. */ #include #include #include #include #include double gsl_cdf_binomial_P(const long k, const long n, const double p) { double P; double a; double b; if(p > 1.0 || p < 0.0) { GSL_CDF_ERROR("p < 0 or p > 1",GSL_EDOM); } if ( k >= n ) { P = 1.0; } else if (k < 0) { P = 0.0; } else { a = (double) k+1; b = (double) n - k; P = gsl_cdf_beta_Q( p, a, b); } return P; } double gsl_cdf_binomial_Q(const long k, const long n, const double q) { double P; double a; double b; if(q > 1.0 || q < 0.0) { GSL_CDF_ERROR("p < 0 or p > 1",GSL_EDOM); } if( k >= n ) { P = 0.0; } else if ( k < 0 ) { P = 1.0; } else { a = (double) k+1; b = (double) n - k; P = gsl_cdf_beta_P(q, a, b); } return P; }