| /////////////////////////////////////////////////////////////////////////////// |
| // kurtosis.hpp |
| // |
| // Copyright 2006 Olivier Gygi, Daniel Egloff. Distributed under the Boost |
| // Software License, Version 1.0. (See accompanying file |
| // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) |
| |
| #ifndef BOOST_ACCUMULATORS_STATISTICS_KURTOSIS_HPP_EAN_28_10_2005 |
| #define BOOST_ACCUMULATORS_STATISTICS_KURTOSIS_HPP_EAN_28_10_2005 |
| |
| #include <limits> |
| #include <boost/mpl/placeholders.hpp> |
| #include <boost/accumulators/framework/accumulator_base.hpp> |
| #include <boost/accumulators/framework/extractor.hpp> |
| #include <boost/accumulators/framework/parameters/sample.hpp> |
| #include <boost/accumulators/numeric/functional.hpp> |
| #include <boost/accumulators/framework/depends_on.hpp> |
| #include <boost/accumulators/statistics/mean.hpp> |
| #include <boost/accumulators/statistics/moment.hpp> |
| |
| namespace boost { namespace accumulators |
| { |
| |
| namespace impl |
| { |
| /////////////////////////////////////////////////////////////////////////////// |
| // kurtosis_impl |
| /** |
| @brief Kurtosis estimation |
| |
| The kurtosis of a sample distribution is defined as the ratio of the 4th central moment and the square of the 2nd central |
| moment (the variance) of the samples, minus 3. The term \f$ -3 \f$ is added in order to ensure that the normal distribution |
| has zero kurtosis. The kurtosis can also be expressed by the simple moments: |
| |
| \f[ |
| \hat{g}_2 = |
| \frac |
| {\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} |
| {\left(\widehat{m}_n^{(2)} - \hat{\mu}_n^{2}\right)^2} - 3, |
| \f] |
| |
| 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 |
| \f$ n \f$ samples. |
| */ |
| template<typename Sample> |
| struct kurtosis_impl |
| : accumulator_base |
| { |
| // for boost::result_of |
| typedef typename numeric::functional::average<Sample, Sample>::result_type result_type; |
| |
| kurtosis_impl(dont_care) {} |
| |
| template<typename Args> |
| result_type result(Args const &args) const |
| { |
| return numeric::average( |
| accumulators::moment<4>(args) |
| - 4. * accumulators::moment<3>(args) * mean(args) |
| + 6. * accumulators::moment<2>(args) * mean(args) * mean(args) |
| - 3. * mean(args) * mean(args) * mean(args) * mean(args) |
| , ( accumulators::moment<2>(args) - mean(args) * mean(args) ) |
| * ( accumulators::moment<2>(args) - mean(args) * mean(args) ) |
| ) - 3.; |
| } |
| }; |
| |
| } // namespace impl |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| // tag::kurtosis |
| // |
| namespace tag |
| { |
| struct kurtosis |
| : depends_on<mean, moment<2>, moment<3>, moment<4> > |
| { |
| /// INTERNAL ONLY |
| /// |
| typedef accumulators::impl::kurtosis_impl<mpl::_1> impl; |
| }; |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| // extract::kurtosis |
| // |
| namespace extract |
| { |
| extractor<tag::kurtosis> const kurtosis = {}; |
| |
| BOOST_ACCUMULATORS_IGNORE_GLOBAL(kurtosis) |
| } |
| |
| using extract::kurtosis; |
| |
| // So that kurtosis can be automatically substituted with |
| // weighted_kurtosis when the weight parameter is non-void |
| template<> |
| struct as_weighted_feature<tag::kurtosis> |
| { |
| typedef tag::weighted_kurtosis type; |
| }; |
| |
| template<> |
| struct feature_of<tag::weighted_kurtosis> |
| : feature_of<tag::kurtosis> |
| { |
| }; |
| |
| }} // namespace boost::accumulators |
| |
| #endif |