3 * Copyright (C) 2004 Jason H. Stover.
5 * This program is free software; you can redistribute it and/or modify
6 * it under the terms of the GNU General Public License as published by
7 * the Free Software Foundation; either version 2 of the License, or (at
8 * your option) any later version.
10 * This program is distributed in the hope that it will be useful, but
11 * WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 * General Public License for more details.
15 * You should have received a copy of the GNU General Public License
16 * along with this program; if not, write to the Free Software
17 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
21 * Computes the cumulative distribution function for a binomial
22 * random variable. For a binomial random variable X with n trials
23 * and success probability p,
25 * Pr( X <= k ) = Pr( Y >= p )
27 * where Y is a beta random variable with parameters k+1 and n-k.
31 * W. Feller, "An Introduction to Probability and Its
32 * Applications," volume 1. Wiley, 1968. Exercise 45, page 173,
37 #include <gsl/gsl_math.h>
38 #include <gsl/gsl_errno.h>
39 #include <gsl/gsl_cdf.h>
40 #include "gsl-extras.h"
43 gslextras_cdf_binomial_P(const long k, const long n, const double p)
49 if(p > 1.0 || p < 0.0)
51 GSLEXTRAS_CDF_ERROR("p < 0 or p > 1",GSL_EDOM);
65 P = gsl_cdf_beta_Q( p, a, b);
71 gslextras_cdf_binomial_Q(const long k, const long n, const double q)
77 if(q > 1.0 || q < 0.0)
79 GSLEXTRAS_CDF_ERROR("p < 0 or p > 1",GSL_EDOM);
93 P = gsl_cdf_beta_P(q, a, b);