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

   1 ///////////////////////////////////////////////////////////////////////////////
   2 // kurtosis.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_KURTOSIS_HPP_EAN_28_10_2005
   9 #define BOOST_ACCUMULATORS_STATISTICS_KURTOSIS_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/mean.hpp>
  19 #include <boost/accumulators/statistics/moment.hpp>
  20
  21 namespace boost { namespace accumulators
  22 {
  23
  24 namespace impl
  25 {
  26     ///////////////////////////////////////////////////////////////////////////////
  27     // kurtosis_impl
  28     /**
  29         @brief Kurtosis estimation
  30
  31         The kurtosis of a sample distribution is defined as the ratio of the 4th central moment and the square of the 2nd central
  32         moment (the variance) of the samples, minus 3. The term \f$ -3 \f$ is added in order to ensure that the normal distribution
  33         has zero kurtosis. The kurtosis can also be expressed by the simple moments:
  34
  35         \f[
  36             \hat{g}_2 =
  37                 \frac
  38                 {\widehat{m}_n^{(4)}-4\widehat{m}_n^{(3)}\hat{\mu}_n+6\widehat{m}_n^{(2)}\hat{\mu}_n^2-3\hat{\mu}_n^4}
  39                 {\left(\widehat{m}_n^{(2)} - \hat{\mu}_n^{2}\right)^2} - 3,
  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     template<typename Sample>
  46     struct kurtosis_impl
  47       : accumulator_base
  48     {
  49         // for boost::result_of
  50         typedef typename numeric::functional::fdiv<Sample, Sample>::result_type result_type;
  51
  52         kurtosis_impl(dont_care) {}
  53
  54         template<typename Args>
  55         result_type result(Args const &args) const
  56         {
  57             return numeric::fdiv(
  58                         accumulators::moment<4>(args)
  59                         - 4. * accumulators::moment<3>(args) * mean(args)
  60                         + 6. * accumulators::moment<2>(args) * mean(args) * mean(args)
  61                         - 3. * mean(args) * mean(args) * mean(args) * mean(args)
  62                       , ( accumulators::moment<2>(args) - mean(args) * mean(args) )
  63                         * ( accumulators::moment<2>(args) - mean(args) * mean(args) )
  64                     ) - 3.;
  65         }
  66     };
  67
  68 } // namespace impl
  69
  70 ///////////////////////////////////////////////////////////////////////////////
  71 // tag::kurtosis
  72 //
  73 namespace tag
  74 {
  75     struct kurtosis
  76       : depends_on<mean, moment<2>, moment<3>, moment<4> >
  77     {
  78         /// INTERNAL ONLY
  79         ///
  80         typedef accumulators::impl::kurtosis_impl<mpl::_1> impl;
  81     };
  82 }
  83
  84 ///////////////////////////////////////////////////////////////////////////////
  85 // extract::kurtosis
  86 //
  87 namespace extract
  88 {
  89     extractor<tag::kurtosis> const kurtosis = {};
  90
  91     BOOST_ACCUMULATORS_IGNORE_GLOBAL(kurtosis)
  92 }
  93
  94 using extract::kurtosis;
  95
  96 // So that kurtosis can be automatically substituted with
  97 // weighted_kurtosis when the weight parameter is non-void
  98 template<>
  99 struct as_weighted_feature<tag::kurtosis>
 100 {
 101     typedef tag::weighted_kurtosis type;
 102 };
 103
 104 template<>
 105 struct feature_of<tag::weighted_kurtosis>
 106   : feature_of<tag::kurtosis>
 107 {
 108 };
 109
 110 }} // namespace boost::accumulators
 111
 112 #endif