1///////////////////////////////////////////////////////////////////////////////
2// skewness.hpp
3//
4// Copyright 2006 Olivier Gygi, Daniel Egloff. Distributed under the Boost
5// Software License, Version 1.0. (See accompanying file
6// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
7
8#ifndef BOOST_ACCUMULATORS_STATISTICS_SKEWNESS_HPP_EAN_28_10_2005
9#define BOOST_ACCUMULATORS_STATISTICS_SKEWNESS_HPP_EAN_28_10_2005
10
11#include <limits>
12#include <boost/mpl/placeholders.hpp>
13#include <boost/accumulators/framework/accumulator_base.hpp>
14#include <boost/accumulators/framework/extractor.hpp>
15#include <boost/accumulators/framework/parameters/sample.hpp>
16#include <boost/accumulators/numeric/functional.hpp>
17#include <boost/accumulators/framework/depends_on.hpp>
18#include <boost/accumulators/statistics_fwd.hpp>
19#include <boost/accumulators/statistics/moment.hpp>
20#include <boost/accumulators/statistics/mean.hpp>
21
22
23namespace boost { namespace accumulators
24{
25
26namespace impl
27{
28 ///////////////////////////////////////////////////////////////////////////////
29 // skewness_impl
30 /**
31 @brief Skewness estimation
32
33 The skewness of a sample distribution is defined as the ratio of the 3rd central moment and the \f$ 3/2 \f$-th power
34 of the 2nd central moment (the variance) of the samples 3. The skewness can also be expressed by the simple moments:
35
36 \f[
37 \hat{g}_1 =
38 \frac
39 {\widehat{m}_n^{(3)}-3\widehat{m}_n^{(2)}\hat{\mu}_n+2\hat{\mu}_n^3}
40 {\left(\widehat{m}_n^{(2)} - \hat{\mu}_n^{2}\right)^{3/2}}
41 \f]
42
43 where \f$ \widehat{m}_n^{(i)} \f$ are the \f$ i \f$-th moment and \f$ \hat{\mu}_n \f$ the mean (first moment) of the
44 \f$ n \f$ samples.
45 */
46 template<typename Sample>
47 struct skewness_impl
48 : accumulator_base
49 {
50 // for boost::result_of
51 typedef typename numeric::functional::fdiv<Sample, Sample>::result_type result_type;
52
53 skewness_impl(dont_care)
54 {
55 }
56
57 template<typename Args>
58 result_type result(Args const &args) const
59 {
60 return numeric::fdiv(
61 accumulators::moment<3>(args)
62 - 3. * accumulators::moment<2>(args) * mean(args)
63 + 2. * mean(args) * mean(args) * mean(args)
64 , ( accumulators::moment<2>(args) - mean(args) * mean(args) )
65 * std::sqrt( accumulators::moment<2>(args) - mean(args) * mean(args) )
66 );
67 }
68
69 // serialization is done by accumulators it depends on
70 template<class Archive>
71 void serialize(Archive & ar, const unsigned int file_version) {}
72 };
73
74} // namespace impl
75
76///////////////////////////////////////////////////////////////////////////////
77// tag::skewness
78//
79namespace tag
80{
81 struct skewness
82 : depends_on<mean, moment<2>, moment<3> >
83 {
84 /// INTERNAL ONLY
85 ///
86 typedef accumulators::impl::skewness_impl<mpl::_1> impl;
87 };
88}
89
90///////////////////////////////////////////////////////////////////////////////
91// extract::skewness
92//
93namespace extract
94{
95 extractor<tag::skewness> const skewness = {};
96
97 BOOST_ACCUMULATORS_IGNORE_GLOBAL(skewness)
98}
99
100using extract::skewness;
101
102// So that skewness can be automatically substituted with
103// weighted_skewness when the weight parameter is non-void
104template<>
105struct as_weighted_feature<tag::skewness>
106{
107 typedef tag::weighted_skewness type;
108};
109
110template<>
111struct feature_of<tag::weighted_skewness>
112 : feature_of<tag::skewness>
113{
114};
115
116}} // namespace boost::accumulators
117
118#endif
119

source code of boost/libs/accumulators/include/boost/accumulators/statistics/skewness.hpp