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- /* randist/exppow.c
- *
- * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2006, 2007 James Theiler, Brian Gough
- * Copyright (C) 2006 Giulio Bottazzi
- *
- * 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 exponential power probability distribution is
- p(x) dx = (1/(2 a Gamma(1+1/b))) * exp(-|x/a|^b) dx
- for -infty < x < infty. For b = 1 it reduces to the Laplace
- distribution.
- The exponential power distribution is related to the gamma
- distribution by E = a * pow(G(1/b),1/b), where E is an exponential
- power variate and G is a gamma variate.
- We use this relation for b < 1. For b >=1 we use rejection methods
- based on the laplace and gaussian distributions which should be
- faster. For b>4 we revert to the gamma method.
- See P. R. Tadikamalla, "Random Sampling from the Exponential Power
- Distribution", Journal of the American Statistical Association,
- September 1980, Volume 75, Number 371, pages 683-686.
-
- */
- double
- gsl_ran_exppow (const gsl_rng * r, const double a, const double b)
- {
- if (b < 1 || b > 4)
- {
- double u = gsl_rng_uniform (r);
- double v = gsl_ran_gamma (r, 1 / b, 1.0);
- double z = a * pow (v, 1 / b);
- if (u > 0.5)
- {
- return z;
- }
- else
- {
- return -z;
- }
- }
- else if (b == 1)
- {
- /* Laplace distribution */
- return gsl_ran_laplace (r, a);
- }
- else if (b < 2)
- {
- /* Use laplace distribution for rejection method, from Tadikamalla */
- double x, h, u;
- double B = pow (1 / b, 1 / b);
- do
- {
- x = gsl_ran_laplace (r, B);
- u = gsl_rng_uniform_pos (r);
- h = -pow (fabs (x), b) + fabs (x) / B - 1 + (1 / b);
- }
- while (log (u) > h);
- return a * x;
- }
- else if (b == 2)
- {
- /* Gaussian distribution */
- return gsl_ran_gaussian (r, a / sqrt (2.0));
- }
- else
- {
- /* Use gaussian for rejection method, from Tadikamalla */
- double x, h, u;
- double B = pow (1 / b, 1 / b);
- do
- {
- x = gsl_ran_gaussian (r, B);
- u = gsl_rng_uniform_pos (r);
- h = -pow (fabs (x), b) + (x * x) / (2 * B * B) + (1 / b) - 0.5;
- }
- while (log (u) > h);
- return a * x;
- }
- }
- double
- gsl_ran_exppow_pdf (const double x, const double a, const double b)
- {
- double p;
- double lngamma = gsl_sf_lngamma (1 + 1 / b);
- p = (1 / (2 * a)) * exp (-pow (fabs (x / a), b) - lngamma);
- return p;
- }
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