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1 | /////////////////////////////////////////////////////////////////////////////// |
2 | // weighted_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_WEIGHTED_KURTOSIS_HPP_EAN_28_10_2005 | |
9 | #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_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_fwd.hpp> | |
19 | #include <boost/accumulators/statistics/weighted_moment.hpp> | |
20 | #include <boost/accumulators/statistics/weighted_mean.hpp> | |
21 | ||
22 | namespace boost { namespace accumulators | |
23 | { | |
24 | ||
25 | namespace impl | |
26 | { | |
27 | /////////////////////////////////////////////////////////////////////////////// | |
28 | // weighted_kurtosis_impl | |
29 | /** | |
30 | @brief Kurtosis estimation for weighted samples | |
31 | ||
32 | The kurtosis of a sample distribution is defined as the ratio of the 4th central moment and the square of the 2nd central | |
33 | moment (the variance) of the samples, minus 3. The term \f$ -3 \f$ is added in order to ensure that the normal distribution | |
34 | has zero kurtosis. The kurtosis can also be expressed by the simple moments: | |
35 | ||
36 | \f[ | |
37 | \hat{g}_2 = | |
38 | \frac | |
39 | {\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} | |
40 | {\left(\widehat{m}_n^{(2)} - \hat{\mu}_n^{2}\right)^2} - 3, | |
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 | The kurtosis estimator for weighted samples is formally identical to the estimator for unweighted samples, except that | |
47 | the weighted counterparts of all measures it depends on are to be taken. | |
48 | */ | |
49 | template<typename Sample, typename Weight> | |
50 | struct weighted_kurtosis_impl | |
51 | : accumulator_base | |
52 | { | |
53 | typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample; | |
54 | // for boost::result_of | |
55 | typedef typename numeric::functional::fdiv<weighted_sample, weighted_sample>::result_type result_type; | |
56 | ||
57 | weighted_kurtosis_impl(dont_care) | |
58 | { | |
59 | } | |
60 | ||
61 | template<typename Args> | |
62 | result_type result(Args const &args) const | |
63 | { | |
64 | return numeric::fdiv( | |
65 | accumulators::weighted_moment<4>(args) | |
66 | - 4. * accumulators::weighted_moment<3>(args) * weighted_mean(args) | |
67 | + 6. * accumulators::weighted_moment<2>(args) * weighted_mean(args) * weighted_mean(args) | |
68 | - 3. * weighted_mean(args) * weighted_mean(args) * weighted_mean(args) * weighted_mean(args) | |
69 | , ( accumulators::weighted_moment<2>(args) - weighted_mean(args) * weighted_mean(args) ) | |
70 | * ( accumulators::weighted_moment<2>(args) - weighted_mean(args) * weighted_mean(args) ) | |
71 | ) - 3.; | |
72 | } | |
73 | }; | |
74 | ||
75 | } // namespace impl | |
76 | ||
77 | /////////////////////////////////////////////////////////////////////////////// | |
78 | // tag::weighted_kurtosis | |
79 | // | |
80 | namespace tag | |
81 | { | |
82 | struct weighted_kurtosis | |
83 | : depends_on<weighted_mean, weighted_moment<2>, weighted_moment<3>, weighted_moment<4> > | |
84 | { | |
85 | /// INTERNAL ONLY | |
86 | /// | |
87 | typedef accumulators::impl::weighted_kurtosis_impl<mpl::_1, mpl::_2> impl; | |
88 | }; | |
89 | } | |
90 | ||
91 | /////////////////////////////////////////////////////////////////////////////// | |
92 | // extract::weighted_kurtosis | |
93 | // | |
94 | namespace extract | |
95 | { | |
96 | extractor<tag::weighted_kurtosis> const weighted_kurtosis = {}; | |
97 | ||
98 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_kurtosis) | |
99 | } | |
100 | ||
101 | using extract::weighted_kurtosis; | |
102 | ||
103 | }} // namespace boost::accumulators | |
104 | ||
105 | #endif |