boost/accumulators/statistics/tail_variate_means.hpp
/////////////////////////////////////////////////////////////////////////////// // tail_variate_means.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_VARIATE_MEANS_HPP_DE_01_01_2006 #define BOOST_ACCUMULATORS_STATISTICS_TAIL_VARIATE_MEANS_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/tail.hpp> #include <boost/accumulators/statistics/tail_variate.hpp> #include <boost/accumulators/statistics/tail_mean.hpp> #include <boost/accumulators/statistics/parameters/quantile_probability.hpp> #include <boost/serialization/vector.hpp> #ifdef _MSC_VER # pragma warning(push) # pragma warning(disable: 4127) // conditional expression is constant #endif namespace boost { namespace accumulators { namespace impl { /** @brief Estimation of the absolute and relative tail variate means (for both left and right tails) For all \f$j\f$-th variates associated to the \f$\lceil n(1-\alpha)\rceil\f$ largest samples (or the \f$\lceil n(1-\alpha)\rceil\f$ smallest samples in case of the left tail), the absolute tail means \f$\widehat{ATM}_{n,\alpha}(X, j)\f$ are computed and returned as an iterator range. Alternatively, the relative tail means \f$\widehat{RTM}_{n,\alpha}(X, j)\f$ are returned, which are the absolute tail means normalized with the (non-coherent) sample tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$. \f[ \widehat{ATM}_{n,\alpha}^{\mathrm{right}}(X, j) = \frac{1}{\lceil n(1-\alpha) \rceil} \sum_{i=\lceil \alpha n \rceil}^n \xi_{j,i} \f] \f[ \widehat{ATM}_{n,\alpha}^{\mathrm{left}}(X, j) = \frac{1}{\lceil n\alpha \rceil} \sum_{i=1}^{\lceil n\alpha \rceil} \xi_{j,i} \f] \f[ \widehat{RTM}_{n,\alpha}^{\mathrm{right}}(X, j) = \frac{\sum_{i=\lceil n\alpha \rceil}^n \xi_{j,i}} {\lceil n(1-\alpha)\rceil\widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X)} \f] \f[ \widehat{RTM}_{n,\alpha}^{\mathrm{left}}(X, j) = \frac{\sum_{i=1}^{\lceil n\alpha \rceil} \xi_{j,i}} {\lceil n\alpha\rceil\widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X)} \f] */ /////////////////////////////////////////////////////////////////////////////// // tail_variate_means_impl // by default: absolute tail_variate_means template<typename Sample, typename Impl, typename LeftRight, typename VariateTag> struct tail_variate_means_impl : accumulator_base { typedef typename numeric::functional::fdiv<Sample, std::size_t>::result_type float_type; typedef std::vector<float_type> array_type; // for boost::result_of typedef iterator_range<typename array_type::iterator> result_type; tail_variate_means_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] ) ) ); std::size_t num_variates = tail_variate(args).begin()->size(); this->tail_means_.clear(); this->tail_means_.resize(num_variates, Sample(0)); // 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())) { this->tail_means_ = std::accumulate( tail_variate(args).begin() , tail_variate(args).begin() + n , this->tail_means_ , numeric::plus ); float_type factor = n * ( (is_same<Impl, relative>::value) ? non_coherent_tail_mean(args) : 1. ); std::transform( this->tail_means_.begin() , this->tail_means_.end() , this->tail_means_.begin() #ifdef BOOST_NO_CXX98_BINDERS , std::bind(std::divides<float_type>(), std::placeholders::_1, factor) #else , std::bind2nd(std::divides<float_type>(), factor) #endif ); } else { if (std::numeric_limits<float_type>::has_quiet_NaN) { std::fill( this->tail_means_.begin() , this->tail_means_.end() , std::numeric_limits<float_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 make_iterator_range(this->tail_means_); } // make this accumulator serializeable template<class Archive> void serialize(Archive & ar, const unsigned int file_version) { ar & tail_means_; } private: mutable array_type tail_means_; }; } // namespace impl /////////////////////////////////////////////////////////////////////////////// // tag::absolute_tail_variate_means // tag::relative_tail_variate_means // namespace tag { template<typename LeftRight, typename VariateType, typename VariateTag> struct absolute_tail_variate_means : depends_on<count, non_coherent_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight> > { typedef accumulators::impl::tail_variate_means_impl<mpl::_1, absolute, LeftRight, VariateTag> impl; }; template<typename LeftRight, typename VariateType, typename VariateTag> struct relative_tail_variate_means : depends_on<count, non_coherent_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight> > { typedef accumulators::impl::tail_variate_means_impl<mpl::_1, relative, LeftRight, VariateTag> impl; }; struct abstract_absolute_tail_variate_means : depends_on<> { }; struct abstract_relative_tail_variate_means : depends_on<> { }; } /////////////////////////////////////////////////////////////////////////////// // extract::tail_variate_means // extract::relative_tail_variate_means // namespace extract { extractor<tag::abstract_absolute_tail_variate_means> const tail_variate_means = {}; extractor<tag::abstract_relative_tail_variate_means> const relative_tail_variate_means = {}; BOOST_ACCUMULATORS_IGNORE_GLOBAL(tail_variate_means) BOOST_ACCUMULATORS_IGNORE_GLOBAL(relative_tail_variate_means) } using extract::tail_variate_means; using extract::relative_tail_variate_means; // tail_variate_means<LeftRight, VariateType, VariateTag>(absolute) -> absolute_tail_variate_means<LeftRight, VariateType, VariateTag> template<typename LeftRight, typename VariateType, typename VariateTag> struct as_feature<tag::tail_variate_means<LeftRight, VariateType, VariateTag>(absolute)> { typedef tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> type; }; // tail_variate_means<LeftRight, VariateType, VariateTag>(relative) ->relative_tail_variate_means<LeftRight, VariateType, VariateTag> template<typename LeftRight, typename VariateType, typename VariateTag> struct as_feature<tag::tail_variate_means<LeftRight, VariateType, VariateTag>(relative)> { typedef tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> type; }; // Provides non-templatized extractor template<typename LeftRight, typename VariateType, typename VariateTag> struct feature_of<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> > : feature_of<tag::abstract_absolute_tail_variate_means> { }; // Provides non-templatized extractor template<typename LeftRight, typename VariateType, typename VariateTag> struct feature_of<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> > : feature_of<tag::abstract_relative_tail_variate_means> { }; // So that absolute_tail_means can be automatically substituted // with absolute_weighted_tail_means when the weight parameter is non-void. template<typename LeftRight, typename VariateType, typename VariateTag> struct as_weighted_feature<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> > { typedef tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type; }; template<typename LeftRight, typename VariateType, typename VariateTag> struct feature_of<tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> > : feature_of<tag::absolute_tail_variate_means<LeftRight, VariateType, VariateTag> > { }; // So that relative_tail_means can be automatically substituted // with relative_weighted_tail_means when the weight parameter is non-void. template<typename LeftRight, typename VariateType, typename VariateTag> struct as_weighted_feature<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> > { typedef tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type; }; template<typename LeftRight, typename VariateType, typename VariateTag> struct feature_of<tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> > : feature_of<tag::relative_tail_variate_means<LeftRight, VariateType, VariateTag> > { }; }} // namespace boost::accumulators #ifdef _MSC_VER # pragma warning(pop) #endif #endif