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- /* randist/fdist.c
- *
- * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 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 3 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 "gsl__config.h"
- #include <math.h>
- #include "gsl_sf_gamma.h"
- #include "gsl_rng.h"
- #include "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;
- }
- }
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