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/* statistics/wkurtosis_source.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 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 2 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,wkurtosis) (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,wkurtosis_m_sd)(w, wstride, data, stride, n, wmean, wsd);
}
double
FUNCTION(gsl_stats,wkurtosis_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)
{
/* takes a dataset and finds the kurtosis */
long double wavg = 0, kurtosis;
long double W = 0;
size_t i;
/* find the fourth moment the 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 ;
wavg += (x * x * x * x - wavg) * (wi / W);
}
}
kurtosis = wavg - 3.0; /* makes kurtosis zero for a Gaussian */
return kurtosis;
}
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