/* statistics/skew_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,skew) (const BASE data[], const size_t stride, const size_t n)

{

  const double mean = FUNCTION(gsl_stats,mean)(data, stride, n);

  const double sd = FUNCTION(gsl_stats,sd_m)(data, stride, n, mean);

  return FUNCTION(gsl_stats,skew_m_sd)(data, stride, n, mean, sd);

}

double 

FUNCTION(gsl_stats,skew_m_sd) (const BASE data[], 

                               const size_t stride, const size_t n,

                               const double mean, const double sd)

{

  /* takes a dataset and finds the skewness */

  long double skew = 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++)

    {

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

      skew += (x * x * x - skew) / (i + 1);

    }

  return skew;

}