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- /* randist/tdist.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_math.h"
- #include "gsl_sf_gamma.h"
- #include "gsl_rng.h"
- #include "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;
- }
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