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Diffstat (limited to 'gsl-1.9/cdf/binomial.c')
-rw-r--r-- | gsl-1.9/cdf/binomial.c | 108 |
1 files changed, 108 insertions, 0 deletions
diff --git a/gsl-1.9/cdf/binomial.c b/gsl-1.9/cdf/binomial.c new file mode 100644 index 0000000..40a8d58 --- /dev/null +++ b/gsl-1.9/cdf/binomial.c @@ -0,0 +1,108 @@ +/* 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; +} |