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/* 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;
}
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