3 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 James Theiler, Brian Gough
5 * This program is free software; you can redistribute it and/or modify
6 * it under the terms of the GNU General Public License as published by
7 * the Free Software Foundation; either version 3 of the License, or (at
8 * your option) any later version.
10 * This program is distributed in the hope that it will be useful, but
11 * WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 * General Public License for more details.
15 * You should have received a copy of the GNU General Public License
16 * along with this program; if not, write to the Free Software
17 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
22 #include <gsl/gsl_math.h>
23 #include <gsl/gsl_sf_gamma.h>
24 #include <gsl/gsl_rng.h>
25 #include <gsl/gsl_randist.h>
27 /* The t-distribution has the form
29 p(x) dx = (Gamma((nu + 1)/2)/(sqrt(pi nu) Gamma(nu/2))
30 * (1 + (x^2)/nu)^-((nu + 1)/2) dx
32 The method used here is the one described in Knuth */
35 gsl_ran_tdist (const gsl_rng * r, const double nu)
39 double Y1 = gsl_ran_ugaussian (r);
40 double Y2 = gsl_ran_chisq (r, nu);
42 double t = Y1 / sqrt (Y2 / nu);
51 Y1 = gsl_ran_ugaussian (r);
52 Y2 = gsl_ran_exponential (r, 1 / (nu/2 - 1));
54 Z = Y1 * Y1 / (nu - 2);
56 while (1 - Z < 0 || exp (-Y2 - Z) > (1 - Z));
58 /* Note that there is a typo in Knuth's formula, the line below
59 is taken from the original paper of Marsaglia, Mathematics of
60 Computation, 34 (1980), p 234-256 */
62 t = Y1 / sqrt ((1 - 2 / nu) * (1 - Z));
68 gsl_ran_tdist_pdf (const double x, const double nu)
72 double lg1 = gsl_sf_lngamma (nu / 2);
73 double lg2 = gsl_sf_lngamma ((nu + 1) / 2);
75 p = ((exp (lg2 - lg1) / sqrt (M_PI * nu))
76 * pow ((1 + x * x / nu), -(nu + 1) / 2));