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+/* cdf/poisson.c
+ *
+ * Copyright (C) 2004 Jason H. Stover.
+ *
+ * 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., 59 Temple Place, Suite 330, Boston, MA 02111-1307, USA.
+ */
+
+/*
+ * Computes the cumulative distribution function for a Poisson
+ * random variable. For a Poisson random variable X with parameter
+ * mu,
+ *
+ * Pr( X <= k ) = Pr( Y >= p )
+ *
+ * where Y is a gamma random variable with parameters k+1 and 1.
+ *
+ * Reference:
+ *
+ * W. Feller, "An Introduction to Probability and Its
+ * Applications," volume 1. Wiley, 1968. Exercise 46, 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>
+
+#include "error.h"
+
+/*
+ * Pr (X <= k) for a Poisson random variable X.
+ */
+
+double
+gsl_cdf_poisson_P (const unsigned int k, const double mu)
+{
+ double P;
+ double a;
+
+ if (mu <= 0.0)
+ {
+ CDF_ERROR ("mu <= 0", GSL_EDOM);
+ }
+
+ a = (double) k + 1.0;
+ P = gsl_cdf_gamma_Q (mu, a, 1.0);
+
+ return P;
+}
+
+/*
+ * Pr ( X > k ) for a Possion random variable X.
+ */
+
+double
+gsl_cdf_poisson_Q (const unsigned int k, const double mu)
+{
+ double Q;
+ double a;
+
+ if (mu <= 0.0)
+ {
+ CDF_ERROR ("mu <= 0", GSL_EDOM);
+ }
+
+ a = (double) k + 1.0;
+ Q = gsl_cdf_gamma_P (mu, a, 1.0);
+
+ return Q;
+}