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/* cdf/exppow.c
*
* Copyright (C) 2004 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 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_cdf.h>
#include <gsl/gsl_sf_gamma.h>
/* The exponential power density is parametrized according to
p(x) dx = (1/(2 a Gamma(1 + 1/b))) * exp(-|x/a|^b) dx
so that the distribution reads
/ x<0 0.5 - Gamma_inc_P(1/b,|x/a|^b)
P(x) = | x=0 0.5
\ x>0 0.5 + Gamma_inc_P(1/b,|x/a|^b)
for x in (-infty,+infty) */
double
gsl_cdf_exppow_P (const double x, const double a, const double b)
{
const double u = x / a;
if (u < 0)
{
double P = 0.5 * gsl_sf_gamma_inc_Q (1.0 / b, pow (-u, b));
return P;
}
else
{
double P = 0.5 * (1.0 + gsl_sf_gamma_inc_P (1.0 / b, pow (u, b)));
return P;
}
}
double
gsl_cdf_exppow_Q (const double x, const double a, const double b)
{
const double u = x / a;
if (u < 0)
{
double Q = 0.5 * (1.0 + gsl_sf_gamma_inc_P (1.0 / b, pow (-u, b)));
return Q;
}
else
{
double Q = 0.5 * gsl_sf_gamma_inc_Q (1.0 / b, pow (u, b));
return Q;
}
}
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