]>
Commit | Line | Data |
---|---|---|
7c673cae FG |
1 | /////////////////////////////////////////////////////////////////////////////// |
2 | // weighted_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_WEIGHTED_SKEWNESS_HPP_EAN_28_10_2005 | |
9 | #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_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/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_skewness_impl | |
29 | /** | |
30 | @brief Skewness estimation for weighted samples | |
31 | ||
32 | The skewness of a sample distribution is defined as the ratio of the 3rd central moment and the \f$ 3/2 \f$-th power $ | |
33 | of the 2nd central moment (the variance) of the samples. The skewness can also be expressed by the simple moments: | |
34 | ||
35 | \f[ | |
36 | \hat{g}_1 = | |
37 | \frac | |
38 | {\widehat{m}_n^{(3)}-3\widehat{m}_n^{(2)}\hat{\mu}_n+2\hat{\mu}_n^3} | |
39 | {\left(\widehat{m}_n^{(2)} - \hat{\mu}_n^{2}\right)^{3/2}} | |
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 | The skewness estimator for weighted samples is formally identical to the estimator for unweighted samples, except that | |
46 | the weighted counterparts of all measures it depends on are to be taken. | |
47 | */ | |
48 | template<typename Sample, typename Weight> | |
49 | struct weighted_skewness_impl | |
50 | : accumulator_base | |
51 | { | |
52 | typedef typename numeric::functional::multiplies<Sample, Weight>::result_type weighted_sample; | |
53 | // for boost::result_of | |
54 | typedef typename numeric::functional::fdiv<weighted_sample, weighted_sample>::result_type result_type; | |
55 | ||
56 | weighted_skewness_impl(dont_care) {} | |
57 | ||
58 | template<typename Args> | |
59 | result_type result(Args const &args) const | |
60 | { | |
61 | return numeric::fdiv( | |
62 | accumulators::weighted_moment<3>(args) | |
63 | - 3. * accumulators::weighted_moment<2>(args) * weighted_mean(args) | |
64 | + 2. * weighted_mean(args) * weighted_mean(args) * weighted_mean(args) | |
65 | , ( accumulators::weighted_moment<2>(args) - weighted_mean(args) * weighted_mean(args) ) | |
66 | * std::sqrt( accumulators::weighted_moment<2>(args) - weighted_mean(args) * weighted_mean(args) ) | |
67 | ); | |
68 | } | |
69 | }; | |
70 | ||
71 | } // namespace impl | |
72 | ||
73 | /////////////////////////////////////////////////////////////////////////////// | |
74 | // tag::weighted_skewness | |
75 | // | |
76 | namespace tag | |
77 | { | |
78 | struct weighted_skewness | |
79 | : depends_on<weighted_mean, weighted_moment<2>, weighted_moment<3> > | |
80 | { | |
81 | /// INTERNAL ONLY | |
82 | /// | |
83 | typedef accumulators::impl::weighted_skewness_impl<mpl::_1, mpl::_2> impl; | |
84 | }; | |
85 | } | |
86 | ||
87 | /////////////////////////////////////////////////////////////////////////////// | |
88 | // extract::weighted_skewness | |
89 | // | |
90 | namespace extract | |
91 | { | |
92 | extractor<tag::weighted_skewness> const weighted_skewness = {}; | |
93 | ||
94 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_skewness) | |
95 | } | |
96 | ||
97 | using extract::weighted_skewness; | |
98 | ||
99 | }} // namespace boost::accumulators | |
100 | ||
101 | #endif |