| /* cdf/binomial.c |
| * |
| * Copyright (C) 2004 Jason H. Stover. |
| * Copyright (C) 2004 Giulio Bottazzi |
| * |
| * 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., 675 Mass Ave, Cambridge, MA 02139, USA. |
| */ |
| |
| #include <config.h> |
| #include <math.h> |
| #include <gsl/gsl_math.h> |
| #include <gsl/gsl_cdf.h> |
| #include <gsl/gsl_sf_gamma.h> |
| |
| #include "error.h" |
| |
| /* 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. |
| |
| The binomial distribution has the form, |
| |
| prob(k) = n!/(k!(n-k)!) * p^k (1-p)^(n-k) for k = 0, 1, ..., n |
| |
| The cumulated distributions can be expressed in terms of normalized |
| incomplete beta functions (see Abramowitz & Stegun eq. 26.5.26 and |
| eq. 6.6.3). |
| |
| Reference: |
| |
| W. Feller, "An Introduction to Probability and Its |
| Applications," volume 1. Wiley, 1968. Exercise 45, 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> |
| |
| double |
| gsl_cdf_binomial_P (const unsigned int k, const double p, const unsigned int n) |
| { |
| double P; |
| double a; |
| double b; |
| |
| if (p > 1.0 || p < 0.0) |
| { |
| CDF_ERROR ("p < 0 or p > 1", GSL_EDOM); |
| } |
| |
| if (k >= n) |
| { |
| P = 1.0; |
| } |
| else |
| { |
| a = (double) k + 1.0; |
| b = (double) n - k; |
| P = gsl_cdf_beta_Q (p, a, b); |
| } |
| |
| return P; |
| } |
| |
| double |
| gsl_cdf_binomial_Q (const unsigned int k, const double p, const unsigned int n) |
| { |
| double Q; |
| double a; |
| double b; |
| |
| if (p > 1.0 || p < 0.0) |
| { |
| CDF_ERROR ("p < 0 or p > 1", GSL_EDOM); |
| } |
| |
| if (k >= n) |
| { |
| Q = 0.0; |
| } |
| else |
| { |
| a = (double) k + 1.0; |
| b = (double) n - k; |
| Q = gsl_cdf_beta_P (p, a, b); |
| } |
| |
| return Q; |
| } |