| /* statistics/skew_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,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; |
| } |
| |
