3 * Copyright (C) 2004 Free Software Foundation, Inc.
4 * Written by Jason H. Stover.
6 * This program is free software; you can redistribute it and/or modify
7 * it under the terms of the GNU General Public License as published by
8 * the Free Software Foundation; either version 2 of the License, or (at
9 * your option) any later version.
11 * This program is distributed in the hope that it will be useful, but
12 * WITHOUT ANY WARRANTY; without even the implied warranty of
13 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 * General Public License for more details.
16 * You should have received a copy of the GNU General Public License
17 * along with this program; if not, write to the Free Software
18 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
22 * Computes the cumulative distribution function for a binomial
23 * random variable. For a binomial random variable X with n trials
24 * and success probability p,
26 * Pr( X <= k ) = Pr( Y >= p )
28 * where Y is a beta random variable with parameters k+1 and n-k.
32 * W. Feller, "An Introduction to Probability and Its
33 * Applications," volume 1. Wiley, 1968. Exercise 45, page 173,
38 #include <gsl/gsl_math.h>
39 #include <gsl/gsl_errno.h>
40 #include <gsl/gsl_cdf.h>
41 #include "gsl-extras.h"
44 gslextras_cdf_binomial_P(const long k, const long n, const double p)
50 if(p > 1.0 || p < 0.0)
52 GSLEXTRAS_CDF_ERROR("p < 0 or p > 1",GSL_EDOM);
66 P = gsl_cdf_beta_Q( p, a, b);
72 gslextras_cdf_binomial_Q(const long k, const long n, const double q)
78 if(q > 1.0 || q < 0.0)
80 GSLEXTRAS_CDF_ERROR("p < 0 or p > 1",GSL_EDOM);
94 P = gsl_cdf_beta_P(q, a, b);