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/* randist/beta.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_rng.h>
#include <gsl/gsl_randist.h>
#include <gsl/gsl_sf_gamma.h>
/* The beta distribution has the form
p(x) dx = (Gamma(a + b)/(Gamma(a) Gamma(b))) x^(a-1) (1-x)^(b-1) dx
The method used here is the one described in Knuth */
double
gsl_ran_beta (const gsl_rng * r, const double a, const double b)
{
double x1 = gsl_ran_gamma (r, a, 1.0);
double x2 = gsl_ran_gamma (r, b, 1.0);
return x1 / (x1 + x2);
}
double
gsl_ran_beta_pdf (const double x, const double a, const double b)
{
if (x < 0 || x > 1)
{
return 0 ;
}
else
{
double p;
double gab = gsl_sf_lngamma (a + b);
double ga = gsl_sf_lngamma (a);
double gb = gsl_sf_lngamma (b);
if (x == 0.0 || x == 1.0)
{
p = exp (gab - ga - gb) * pow (x, a - 1) * pow (1 - x, b - 1);
}
else
{
p = exp (gab - ga - gb + log(x) * (a - 1) + log1p(-x) * (b - 1));
}
return p;
}
}
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