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 = {}; |
97 | |
98 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_kurtosis) |
99 | } |
100 | |
101 | using extract::weighted_kurtosis; |
102 | |
103 | }} // namespace boost::accumulators |
104 | |
105 | #endif |
106 | |