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