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/* 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;
}
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