/* 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 <config.h>

#include <math.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_sf_gamma.h>

#include <gsl/gsl_rng.h>

#include <gsl/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;

}