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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 | ||
68 | } // namespace impl | |
69 | ||
70 | /////////////////////////////////////////////////////////////////////////////// | |
71 | // tag::kurtosis | |
72 | // | |
73 | namespace tag | |
74 | { | |
75 | struct kurtosis | |
76 | : depends_on<mean, moment<2>, moment<3>, moment<4> > | |
77 | { | |
78 | /// INTERNAL ONLY | |
79 | /// | |
80 | typedef accumulators::impl::kurtosis_impl<mpl::_1> impl; | |
81 | }; | |
82 | } | |
83 | ||
84 | /////////////////////////////////////////////////////////////////////////////// | |
85 | // extract::kurtosis | |
86 | // | |
87 | namespace extract | |
88 | { | |
89 | extractor<tag::kurtosis> const kurtosis = {}; | |
90 | ||
91 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(kurtosis) | |
92 | } | |
93 | ||
94 | using extract::kurtosis; | |
95 | ||
96 | // So that kurtosis can be automatically substituted with | |
97 | // weighted_kurtosis when the weight parameter is non-void | |
98 | template<> | |
99 | struct as_weighted_feature<tag::kurtosis> | |
100 | { | |
101 | typedef tag::weighted_kurtosis type; | |
102 | }; | |
103 | ||
104 | template<> | |
105 | struct feature_of<tag::weighted_kurtosis> | |
106 | : feature_of<tag::kurtosis> | |
107 | { | |
108 | }; | |
109 | ||
110 | }} // namespace boost::accumulators | |
111 | ||
112 | #endif |