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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 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;
+}