boost/accumulators/statistics/tail_mean.hpp
/////////////////////////////////////////////////////////////////////////////// // tail_mean.hpp // // Copyright 2006 Daniel Egloff, Olivier Gygi. 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_TAIL_MEAN_HPP_DE_01_01_2006 #define BOOST_ACCUMULATORS_STATISTICS_TAIL_MEAN_HPP_DE_01_01_2006 #include <numeric> #include <vector> #include <limits> #include <functional> #include <sstream> #include <stdexcept> #include <boost/throw_exception.hpp> #include <boost/parameter/keyword.hpp> #include <boost/mpl/placeholders.hpp> #include <boost/type_traits/is_same.hpp> #include <boost/accumulators/framework/accumulator_base.hpp> #include <boost/accumulators/framework/extractor.hpp> #include <boost/accumulators/numeric/functional.hpp> #include <boost/accumulators/framework/parameters/sample.hpp> #include <boost/accumulators/statistics_fwd.hpp> #include <boost/accumulators/statistics/count.hpp> #include <boost/accumulators/statistics/tail.hpp> #include <boost/accumulators/statistics/tail_quantile.hpp> #include <boost/accumulators/statistics/parameters/quantile_probability.hpp> #ifdef _MSC_VER # pragma warning(push) # pragma warning(disable: 4127) // conditional expression is constant #endif namespace boost { namespace accumulators { namespace impl { /////////////////////////////////////////////////////////////////////////////// // coherent_tail_mean_impl // /** @brief Estimation of the coherent tail mean based on order statistics (for both left and right tails) The coherent tail mean \f$\widehat{CTM}_{n,\alpha}(X)\f$ is equal to the non-coherent tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$ plus a correction term that ensures coherence in case of non-continuous distributions. \f[ \widehat{CTM}_{n,\alpha}^{\mathrm{right}}(X) = \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) + \frac{1}{\lceil n(1-\alpha)\rceil}\hat{q}_{n,\alpha}(X)\left(1 - \alpha - \frac{1}{n}\lceil n(1-\alpha)\rceil \right) \f] \f[ \widehat{CTM}_{n,\alpha}^{\mathrm{left}}(X) = \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) + \frac{1}{\lceil n\alpha\rceil}\hat{q}_{n,\alpha}(X)\left(\alpha - \frac{1}{n}\lceil n\alpha\rceil \right) \f] */ template<typename Sample, typename LeftRight> struct coherent_tail_mean_impl : accumulator_base { typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type; // for boost::result_of typedef float_type result_type; coherent_tail_mean_impl(dont_care) {} template<typename Args> result_type result(Args const &args) const { std::size_t cnt = count(args); std::size_t n = static_cast<std::size_t>( std::ceil( cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] ) ) ); extractor<tag::non_coherent_tail_mean<LeftRight> > const some_non_coherent_tail_mean = {}; return some_non_coherent_tail_mean(args) + numeric::fdiv(quantile(args), n) * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] - numeric::fdiv(n, count(args)) ); } // serialization is done by accumulators it depends on template<class Archive> void serialize(Archive & ar, const unsigned int file_version) {} }; /////////////////////////////////////////////////////////////////////////////// // non_coherent_tail_mean_impl // /** @brief Estimation of the (non-coherent) tail mean based on order statistics (for both left and right tails) An estimation of the non-coherent tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$ is given by the mean of the \f$\lceil n\alpha\rceil\f$ smallest samples (left tail) or the mean of the \f$\lceil n(1-\alpha)\rceil\f$ largest samples (right tail), \f$n\f$ being the total number of samples and \f$\alpha\f$ the quantile level: \f[ \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X) = \frac{1}{\lceil n(1-\alpha)\rceil} \sum_{i=\lceil \alpha n \rceil}^n X_{i:n} \f] \f[ \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X) = \frac{1}{\lceil n\alpha\rceil} \sum_{i=1}^{\lceil \alpha n \rceil} X_{i:n} \f] It thus requires the caching of at least the \f$\lceil n\alpha\rceil\f$ smallest or the \f$\lceil n(1-\alpha)\rceil\f$ largest samples. @param quantile_probability */ template<typename Sample, typename LeftRight> struct non_coherent_tail_mean_impl : accumulator_base { typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type; // for boost::result_of typedef float_type result_type; non_coherent_tail_mean_impl(dont_care) {} template<typename Args> result_type result(Args const &args) const { std::size_t cnt = count(args); std::size_t n = static_cast<std::size_t>( std::ceil( cnt * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] ) ) ); // If n is in a valid range, return result, otherwise return NaN or throw exception if (n <= static_cast<std::size_t>(tail(args).size())) return numeric::fdiv( std::accumulate( tail(args).begin() , tail(args).begin() + n , Sample(0) ) , n ); else { if (std::numeric_limits<result_type>::has_quiet_NaN) { return std::numeric_limits<result_type>::quiet_NaN(); } else { std::ostringstream msg; msg << "index n = " << n << " is not in valid range [0, " << tail(args).size() << ")"; boost::throw_exception(std::runtime_error(msg.str())); return Sample(0); } } } // serialization is done by accumulators it depends on template<class Archive> void serialize(Archive & ar, const unsigned int file_version) {} }; } // namespace impl /////////////////////////////////////////////////////////////////////////////// // tag::coherent_tail_mean<> // tag::non_coherent_tail_mean<> // namespace tag { template<typename LeftRight> struct coherent_tail_mean : depends_on<count, quantile, non_coherent_tail_mean<LeftRight> > { typedef accumulators::impl::coherent_tail_mean_impl<mpl::_1, LeftRight> impl; }; template<typename LeftRight> struct non_coherent_tail_mean : depends_on<count, tail<LeftRight> > { typedef accumulators::impl::non_coherent_tail_mean_impl<mpl::_1, LeftRight> impl; }; struct abstract_non_coherent_tail_mean : depends_on<> { }; } /////////////////////////////////////////////////////////////////////////////// // extract::non_coherent_tail_mean; // extract::coherent_tail_mean; // namespace extract { extractor<tag::abstract_non_coherent_tail_mean> const non_coherent_tail_mean = {}; extractor<tag::tail_mean> const coherent_tail_mean = {}; BOOST_ACCUMULATORS_IGNORE_GLOBAL(non_coherent_tail_mean) BOOST_ACCUMULATORS_IGNORE_GLOBAL(coherent_tail_mean) } using extract::non_coherent_tail_mean; using extract::coherent_tail_mean; // for the purposes of feature-based dependency resolution, // coherent_tail_mean<LeftRight> provides the same feature as tail_mean template<typename LeftRight> struct feature_of<tag::coherent_tail_mean<LeftRight> > : feature_of<tag::tail_mean> { }; template<typename LeftRight> struct feature_of<tag::non_coherent_tail_mean<LeftRight> > : feature_of<tag::abstract_non_coherent_tail_mean> { }; // So that non_coherent_tail_mean can be automatically substituted // with weighted_non_coherent_tail_mean when the weight parameter is non-void. template<typename LeftRight> struct as_weighted_feature<tag::non_coherent_tail_mean<LeftRight> > { typedef tag::non_coherent_weighted_tail_mean<LeftRight> type; }; template<typename LeftRight> struct feature_of<tag::non_coherent_weighted_tail_mean<LeftRight> > : feature_of<tag::non_coherent_tail_mean<LeftRight> > {}; // NOTE that non_coherent_tail_mean cannot be feature-grouped with tail_mean, // which is the base feature for coherent tail means, since (at least for // non-continuous distributions) non_coherent_tail_mean is a different measure! }} // namespace boost::accumulators #ifdef _MSC_VER # pragma warning(pop) #endif #endif