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/* randist/tdist.c
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 James Theiler, Brian Gough
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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#include <config.h>
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#include <math.h>
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#include <gsl/gsl_math.h>
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#include <gsl/gsl_sf_gamma.h>
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#include <gsl/gsl_rng.h>
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#include <gsl/gsl_randist.h>
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/* The t-distribution has the form
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p(x) dx = (Gamma((nu + 1)/2)/(sqrt(pi nu) Gamma(nu/2))
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* (1 + (x^2)/nu)^-((nu + 1)/2) dx
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The method used here is the one described in Knuth */
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double
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gsl_ran_tdist (const gsl_rng * r, const double nu)
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{
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if (nu <= 2)
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{
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double Y1 = gsl_ran_ugaussian (r);
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double Y2 = gsl_ran_chisq (r, nu);
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double t = Y1 / sqrt (Y2 / nu);
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return t;
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}
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else
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{
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double Y1, Y2, Z, t;
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do
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{
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Y1 = gsl_ran_ugaussian (r);
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Y2 = gsl_ran_exponential (r, 1 / (nu/2 - 1));
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Z = Y1 * Y1 / (nu - 2);
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}
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while (1 - Z < 0 || exp (-Y2 - Z) > (1 - Z));
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/* Note that there is a typo in Knuth's formula, the line below
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is taken from the original paper of Marsaglia, Mathematics of
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Computation, 34 (1980), p 234-256 */
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t = Y1 / sqrt ((1 - 2 / nu) * (1 - Z));
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return t;
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}
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}
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double
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gsl_ran_tdist_pdf (const double x, const double nu)
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{
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double p;
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double lg1 = gsl_sf_lngamma (nu / 2);
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double lg2 = gsl_sf_lngamma ((nu + 1) / 2);
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p = ((exp (lg2 - lg1) / sqrt (M_PI * nu))
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* pow ((1 + x * x / nu), -(nu + 1) / 2));
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return p;
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}
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