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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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