text: /* 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 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 <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;
      }
  }
  