/* statistics/wskew_source.c

 * 

 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Jim Davies, Brian Gough

 * 

 * 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.

 */

double 

FUNCTION(gsl_stats,wskew) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n)

{

  const double wmean = FUNCTION(gsl_stats,wmean)(w, wstride, data, stride, n);

  const double wsd = FUNCTION(gsl_stats,wsd_m)(w, wstride, data, stride, n, wmean);

  return FUNCTION(gsl_stats,wskew_m_sd)(w, wstride, data, stride, n, wmean, wsd);

}

double 

FUNCTION(gsl_stats,wskew_m_sd) (const BASE w[], const size_t wstride, 

                                const BASE data[], 

                                const size_t stride, const size_t n,

                                const double wmean, const double wsd)

{

  /* Compute the weighted skewness of a dataset */

  long double wskew = 0;

  long double W = 0;

  size_t i;

  /* find the sum of the cubed deviations, normalized by the sd. */

  /* we use a recurrence relation to stably update a running value so

     there aren't any large sums that can overflow */

  for (i = 0; i < n; i++)

    {

      BASE wi = w[i * wstride];

      if (wi > 0) {

        const long double x = (data[i * stride] - wmean) / wsd;

        W += wi ;

        wskew += (x * x * x - wskew) * (wi / W);

      }

    }

  return wskew;

}