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/////////////////////////////////////////////////////////////////////////////// // 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 #include #include #include #include #include #include #include #include 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 struct kurtosis_impl : accumulator_base { // for boost::result_of typedef typename numeric::functional::fdiv::result_type result_type; kurtosis_impl(dont_care) {} template result_type result(Args const &args) const { return numeric::fdiv( 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.; } // serialization is done by accumulators it depends on template void serialize(Archive & ar, const unsigned int file_version) {} }; } // namespace impl /////////////////////////////////////////////////////////////////////////////// // tag::kurtosis // namespace tag { struct kurtosis : depends_on, moment<3>, moment<4> > { /// INTERNAL ONLY /// typedef accumulators::impl::kurtosis_impl impl; }; } /////////////////////////////////////////////////////////////////////////////// // extract::kurtosis // namespace extract { extractor 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 { typedef tag::weighted_kurtosis type; }; template<> struct feature_of : feature_of { }; }} // namespace boost::accumulators #endif