1 /////////////////////////////////////////////////////////////////////////////// 2 // 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_SKEWNESS_HPP_EAN_28_10_2005 9 #define BOOST_ACCUMULATORS_STATISTICS_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/moment.hpp> 20 #include <boost/accumulators/statistics/mean.hpp> 21 22 23 namespace boost { namespace accumulators 24 { 25 26 namespace impl 27 { 28 /////////////////////////////////////////////////////////////////////////////// 29 // skewness_impl 30 /** 31 @brief Skewness estimation 32 33 The skewness of a sample distribution is defined as the ratio of the 3rd central moment and the \f$ 3/2 \f$-th power 34 of the 2nd central moment (the variance) of the samples 3. The skewness can also be expressed by the simple moments: 35 36 \f[ 37 \hat{g}_1 = 38 \frac 39 {\widehat{m}_n^{(3)}-3\widehat{m}_n^{(2)}\hat{\mu}_n+2\hat{\mu}_n^3} 40 {\left(\widehat{m}_n^{(2)} - \hat{\mu}_n^{2}\right)^{3/2}} 41 \f] 42 43 where \f$ \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 template<typename Sample> 47 struct skewness_impl 48 : accumulator_base 49 { 50 // for boost::result_of 51 typedef typename numeric::functional::fdiv<Sample, Sample>::result_type result_type; 52 skewness_implboost::accumulators::impl::skewness_impl53 skewness_impl(dont_care) 54 { 55 } 56 57 template<typename Args> resultboost::accumulators::impl::skewness_impl58 result_type result(Args const &args) const 59 { 60 return numeric::fdiv( 61 accumulators::moment<3>(args) 62 - 3. * accumulators::moment<2>(args) * mean(args) 63 + 2. * mean(args) * mean(args) * mean(args) 64 , ( accumulators::moment<2>(args) - mean(args) * mean(args) ) 65 * std::sqrt( accumulators::moment<2>(args) - mean(args) * mean(args) ) 66 ); 67 } 68 69 // serialization is done by accumulators it depends on 70 template<class Archive> serializeboost::accumulators::impl::skewness_impl71 void serialize(Archive & ar, const unsigned int file_version) {} 72 }; 73 74 } // namespace impl 75 76 /////////////////////////////////////////////////////////////////////////////// 77 // tag::skewness 78 // 79 namespace tag 80 { 81 struct skewness 82 : depends_on<mean, moment<2>, moment<3> > 83 { 84 /// INTERNAL ONLY 85 /// 86 typedef accumulators::impl::skewness_impl<mpl::_1> impl; 87 }; 88 } 89 90 /////////////////////////////////////////////////////////////////////////////// 91 // extract::skewness 92 // 93 namespace extract 94 { 95 extractor<tag::skewness> const skewness = {}; 96 97 BOOST_ACCUMULATORS_IGNORE_GLOBAL(skewness) 98 } 99 100 using extract::skewness; 101 102 // So that skewness can be automatically substituted with 103 // weighted_skewness when the weight parameter is non-void 104 template<> 105 struct as_weighted_feature<tag::skewness> 106 { 107 typedef tag::weighted_skewness type; 108 }; 109 110 template<> 111 struct feature_of<tag::weighted_skewness> 112 : feature_of<tag::skewness> 113 { 114 }; 115 116 }} // namespace boost::accumulators 117 118 #endif 119