| /* randist/fdist.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_sf_gamma.h> |
| #include <gsl/gsl_rng.h> |
| #include <gsl/gsl_randist.h> |
| |
| /* The F distribution has the form |
| |
| p(x) dx = (nu1^(nu1/2) nu2^(nu2/2) Gamma((nu1 + nu2)/2) / |
| Gamma(nu1/2) Gamma(nu2/2)) * |
| x^(nu1/2 - 1) (nu2 + nu1 * x)^(-nu1/2 -nu2/2) dx |
| |
| The method used here is the one described in Knuth */ |
| |
| double |
| gsl_ran_fdist (const gsl_rng * r, const double nu1, const double nu2) |
| { |
| |
| double Y1 = gsl_ran_gamma (r, nu1 / 2, 2.0); |
| double Y2 = gsl_ran_gamma (r, nu2 / 2, 2.0); |
| |
| double f = (Y1 * nu2) / (Y2 * nu1); |
| |
| return f; |
| } |
| |
| double |
| gsl_ran_fdist_pdf (const double x, const double nu1, const double nu2) |
| { |
| if (x < 0) |
| { |
| return 0 ; |
| } |
| else |
| { |
| double p; |
| double lglg = (nu1 / 2) * log (nu1) + (nu2 / 2) * log (nu2) ; |
| |
| double lg12 = gsl_sf_lngamma ((nu1 + nu2) / 2); |
| double lg1 = gsl_sf_lngamma (nu1 / 2); |
| double lg2 = gsl_sf_lngamma (nu2 / 2); |
| |
| p = exp (lglg + lg12 - lg1 - lg2) |
| * pow (x, nu1 / 2 - 1) * pow (nu2 + nu1 * x, -nu1 / 2 - nu2 / 2); |
| |
| return p; |
| } |
| } |