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+/* randist/tdist.c
+ *
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000 James Theiler, Brian Gough
+ *
+ * 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <math.h>
+#include <gsl/gsl_math.h>
+#include <gsl/gsl_sf_gamma.h>
+#include <gsl/gsl_rng.h>
+#include <gsl/gsl_randist.h>
+
+/* The t-distribution has the form
+
+ p(x) dx = (Gamma((nu + 1)/2)/(sqrt(pi nu) Gamma(nu/2))
+ * (1 + (x^2)/nu)^-((nu + 1)/2) dx
+
+ The method used here is the one described in Knuth */
+
+double
+gsl_ran_tdist (const gsl_rng * r, const double nu)
+{
+ if (nu <= 2)
+ {
+ double Y1 = gsl_ran_ugaussian (r);
+ double Y2 = gsl_ran_chisq (r, nu);
+
+ double t = Y1 / sqrt (Y2 / nu);
+
+ return t;
+ }
+ else
+ {
+ double Y1, Y2, Z, t;
+ do
+ {
+ Y1 = gsl_ran_ugaussian (r);
+ Y2 = gsl_ran_exponential (r, 1 / (nu/2 - 1));
+
+ Z = Y1 * Y1 / (nu - 2);
+ }
+ while (1 - Z < 0 || exp (-Y2 - Z) > (1 - Z));
+
+ /* Note that there is a typo in Knuth's formula, the line below
+ is taken from the original paper of Marsaglia, Mathematics of
+ Computation, 34 (1980), p 234-256 */
+
+ t = Y1 / sqrt ((1 - 2 / nu) * (1 - Z));
+ return t;
+ }
+}
+
+double
+gsl_ran_tdist_pdf (const double x, const double nu)
+{
+ double p;
+
+ double lg1 = gsl_sf_lngamma (nu / 2);
+ double lg2 = gsl_sf_lngamma ((nu + 1) / 2);
+
+ p = ((exp (lg2 - lg1) / sqrt (M_PI * nu))
+ * pow ((1 + x * x / nu), -(nu + 1) / 2));
+ return p;
+}
+
+