ceph/src/boost/libs/accumulators/include/boost/accumulators/statistics/skewness.hpp

   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
  53         skewness_impl(dont_care)
  54         {
  55         }
  56
  57         template<typename Args>
  58         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
  70 } // namespace impl
  71
  72 ///////////////////////////////////////////////////////////////////////////////
  73 // tag::skewness
  74 //
  75 namespace tag
  76 {
  77     struct skewness
  78       : depends_on<mean, moment<2>, moment<3> >
  79     {
  80         /// INTERNAL ONLY
  81         ///
  82         typedef accumulators::impl::skewness_impl<mpl::_1> impl;
  83     };
  84 }
  85
  86 ///////////////////////////////////////////////////////////////////////////////
  87 // extract::skewness
  88 //
  89 namespace extract
  90 {
  91     extractor<tag::skewness> const skewness = {};
  92
  93     BOOST_ACCUMULATORS_IGNORE_GLOBAL(skewness)
  94 }
  95
  96 using extract::skewness;
  97
  98 // So that skewness can be automatically substituted with
  99 // weighted_skewness when the weight parameter is non-void
 100 template<>
 101 struct as_weighted_feature<tag::skewness>
 102 {
 103     typedef tag::weighted_skewness type;
 104 };
 105
 106 template<>
 107 struct feature_of<tag::weighted_skewness>
 108   : feature_of<tag::skewness>
 109 {
 110 };
 111
 112 }} // namespace boost::accumulators
 113
 114 #endif