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Diffstat (limited to 'gsl-1.9/randist/tdist.c')
-rw-r--r-- | gsl-1.9/randist/tdist.c | 80 |
1 files changed, 80 insertions, 0 deletions
diff --git a/gsl-1.9/randist/tdist.c b/gsl-1.9/randist/tdist.c new file mode 100644 index 0000000..f2703c8 --- /dev/null +++ b/gsl-1.9/randist/tdist.c @@ -0,0 +1,80 @@ +/* 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; +} + + |