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- /* 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 3 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 "gsl__config.h"
- #include <math.h>
- #include "gsl_math.h"
- #include "gsl_cdf.h"
- #include "gsl_sf_gamma.h"
- #include "gsl_cdf__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 "gsl__config.h"
- #include <math.h>
- #include "gsl_math.h"
- #include "gsl_errno.h"
- #include "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;
- }
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