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

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