| /* 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; |
| } |
| |
| |