1 | /////////////////////////////////////////////////////////////////////////////// |
2 | // kurtosis.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_KURTOSIS_HPP_EAN_28_10_2005 |
9 | #define BOOST_ACCUMULATORS_STATISTICS_KURTOSIS_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/mean.hpp> |
19 | #include <boost/accumulators/statistics/moment.hpp> |
20 | |
21 | namespace boost { namespace accumulators |
22 | { |
23 | |
24 | namespace impl |
25 | { |
26 | /////////////////////////////////////////////////////////////////////////////// |
27 | // kurtosis_impl |
28 | /** |
29 | @brief Kurtosis estimation |
30 | |
31 | The kurtosis of a sample distribution is defined as the ratio of the 4th central moment and the square of the 2nd central |
32 | moment (the variance) of the samples, minus 3. The term \f$ -3 \f$ is added in order to ensure that the normal distribution |
33 | has zero kurtosis. The kurtosis can also be expressed by the simple moments: |
34 | |
35 | \f[ |
36 | \hat{g}_2 = |
37 | \frac |
38 | {\widehat{m}_n^{(4)}-4\widehat{m}_n^{(3)}\hat{\mu}_n+6\widehat{m}_n^{(2)}\hat{\mu}_n^2-3\hat{\mu}_n^4} |
39 | {\left(\widehat{m}_n^{(2)} - \hat{\mu}_n^{2}\right)^2} - 3, |
40 | \f] |
41 | |
42 | 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 |
43 | \f$ n \f$ samples. |
44 | */ |
45 | template<typename Sample> |
46 | struct kurtosis_impl |
47 | : accumulator_base |
48 | { |
49 | // for boost::result_of |
50 | typedef typename numeric::functional::fdiv<Sample, Sample>::result_type result_type; |
51 | |
52 | kurtosis_impl(dont_care) {} |
53 | |
54 | template<typename Args> |
55 | result_type result(Args const &args) const |
56 | { |
57 | return numeric::fdiv( |
58 | accumulators::moment<4>(args) |
59 | - 4. * accumulators::moment<3>(args) * mean(args) |
60 | + 6. * accumulators::moment<2>(args) * mean(args) * mean(args) |
61 | - 3. * mean(args) * mean(args) * mean(args) * mean(args) |
62 | , ( accumulators::moment<2>(args) - mean(args) * mean(args) ) |
63 | * ( accumulators::moment<2>(args) - mean(args) * mean(args) ) |
64 | ) - 3.; |
65 | } |
66 | |
67 | // serialization is done by accumulators it depends on |
68 | template<class Archive> |
69 | void serialize(Archive & ar, const unsigned int file_version) {} |
70 | }; |
71 | |
72 | } // namespace impl |
73 | |
74 | /////////////////////////////////////////////////////////////////////////////// |
75 | // tag::kurtosis |
76 | // |
77 | namespace tag |
78 | { |
79 | struct kurtosis |
80 | : depends_on<mean, moment<2>, moment<3>, moment<4> > |
81 | { |
82 | /// INTERNAL ONLY |
83 | /// |
84 | typedef accumulators::impl::kurtosis_impl<mpl::_1> impl; |
85 | }; |
86 | } |
87 | |
88 | /////////////////////////////////////////////////////////////////////////////// |
89 | // extract::kurtosis |
90 | // |
91 | namespace extract |
92 | { |
93 | extractor<tag::kurtosis> const = {}; |
94 | |
95 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(kurtosis) |
96 | } |
97 | |
98 | using extract::kurtosis; |
99 | |
100 | // So that kurtosis can be automatically substituted with |
101 | // weighted_kurtosis when the weight parameter is non-void |
102 | template<> |
103 | struct as_weighted_feature<tag::kurtosis> |
104 | { |
105 | typedef tag::weighted_kurtosis type; |
106 | }; |
107 | |
108 | template<> |
109 | struct feature_of<tag::weighted_kurtosis> |
110 | : feature_of<tag::kurtosis> |
111 | { |
112 | }; |
113 | |
114 | }} // namespace boost::accumulators |
115 | |
116 | #endif |
117 | |