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 | |
23 | namespace boost { namespace accumulators |
24 | { |
25 | |
26 | namespace 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 | // |
79 | namespace 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 | // |
93 | namespace extract |
94 | { |
95 | extractor<tag::skewness> const skewness = {}; |
96 | |
97 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(skewness) |
98 | } |
99 | |
100 | using extract::skewness; |
101 | |
102 | // So that skewness can be automatically substituted with |
103 | // weighted_skewness when the weight parameter is non-void |
104 | template<> |
105 | struct as_weighted_feature<tag::skewness> |
106 | { |
107 | typedef tag::weighted_skewness type; |
108 | }; |
109 | |
110 | template<> |
111 | struct feature_of<tag::weighted_skewness> |
112 | : feature_of<tag::skewness> |
113 | { |
114 | }; |
115 | |
116 | }} // namespace boost::accumulators |
117 | |
118 | #endif |
119 |