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
22namespace boost { namespace accumulators
23{
24
25namespace 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//
76namespace 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//
90namespace extract
91{
92 extractor<tag::weighted_skewness> const weighted_skewness = {};
93
94 BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_skewness)
95}
96
97using extract::weighted_skewness;
98
99}} // namespace boost::accumulators
100
101#endif
102

source code of include/boost/accumulators/statistics/weighted_skewness.hpp