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 = {}; |
93 | |
94 | BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_skewness) |
95 | } |
96 | |
97 | using extract::weighted_skewness; |
98 | |
99 | }} // namespace boost::accumulators |
100 | |
101 | #endif |
102 | |