boost/accumulators/statistics/weighted_tail_variate_means.hpp
/////////////////////////////////////////////////////////////////////////////// // weighted_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_WEIGHTED_TAIL_VARIATE_MEANS_HPP_DE_01_01_2006 #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_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/numeric/functional.hpp> #include <boost/accumulators/framework/accumulator_base.hpp> #include <boost/accumulators/framework/extractor.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_variate_means.hpp> #include <boost/accumulators/statistics/weighted_tail_mean.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 { // for _BinaryOperatrion2 in std::inner_product below // mutliplies two values and promotes the result to double namespace numeric { namespace functional { /////////////////////////////////////////////////////////////////////////////// // numeric::functional::multiply_and_promote_to_double template<typename T, typename U> struct multiply_and_promote_to_double : multiplies<T, double const> { }; }} } namespace boost { namespace accumulators { namespace impl { /** @brief Estimation of the absolute and relative weighted tail variate means (for both left and right tails) For all \f$j\f$-th variates associated to the \f[ \lambda = \inf\left\{ l \left| \frac{1}{\bar{w}_n}\sum_{i=1}^{l} w_i \geq \alpha \right. \right\} \f] smallest samples (left tail) or the weighted mean of the \f[ n + 1 - \rho = n + 1 - \sup\left\{ r \left| \frac{1}{\bar{w}_n}\sum_{i=r}^{n} w_i \geq (1 - \alpha) \right. \right\} \f] largest samples (right tail), the absolute weighted tail means \f$\widehat{ATM}_{n,\alpha}(X, j)\f$ are computed and returned as an iterator range. Alternatively, the relative weighted tail means \f$\widehat{RTM}_{n,\alpha}(X, j)\f$ are returned, which are the absolute weighted tail means normalized with the weighted (non-coherent) sample tail mean \f$\widehat{NCTM}_{n,\alpha}(X)\f$. \f[ \widehat{ATM}_{n,\alpha}^{\mathrm{right}}(X, j) = \frac{1}{\sum_{i=\rho}^n w_i} \sum_{i=\rho}^n w_i \xi_{j,i} \f] \f[ \widehat{ATM}_{n,\alpha}^{\mathrm{left}}(X, j) = \frac{1}{\sum_{i=1}^{\lambda}} \sum_{i=1}^{\lambda} w_i \xi_{j,i} \f] \f[ \widehat{RTM}_{n,\alpha}^{\mathrm{right}}(X, j) = \frac{\sum_{i=\rho}^n w_i \xi_{j,i}} {\sum_{i=\rho}^n w_i \widehat{NCTM}_{n,\alpha}^{\mathrm{right}}(X)} \f] \f[ \widehat{RTM}_{n,\alpha}^{\mathrm{left}}(X, j) = \frac{\sum_{i=1}^{\lambda} w_i \xi_{j,i}} {\sum_{i=1}^{\lambda} w_i \widehat{NCTM}_{n,\alpha}^{\mathrm{left}}(X)} \f] */ /////////////////////////////////////////////////////////////////////////////// // weighted_tail_variate_means_impl // by default: absolute weighted_tail_variate_means template<typename Sample, typename Weight, typename Impl, typename LeftRight, typename VariateType> struct weighted_tail_variate_means_impl : accumulator_base { typedef typename numeric::functional::average<Weight, Weight>::result_type float_type; typedef typename numeric::functional::average<typename numeric::functional::multiplies<VariateType, Weight>::result_type, Weight>::result_type array_type; // for boost::result_of typedef iterator_range<typename array_type::iterator> result_type; weighted_tail_variate_means_impl(dont_care) {} template<typename Args> result_type result(Args const &args) const { float_type threshold = sum_of_weights(args) * ( ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] ); std::size_t n = 0; Weight sum = Weight(0); while (sum < threshold) { if (n < static_cast<std::size_t>(tail_weights(args).size())) { sum += *(tail_weights(args).begin() + n); n++; } 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())); } } } std::size_t num_variates = tail_variate(args).begin()->size(); this->tail_means_.clear(); this->tail_means_.resize(num_variates, Sample(0)); this->tail_means_ = std::inner_product( tail_variate(args).begin() , tail_variate(args).begin() + n , tail_weights(args).begin() , this->tail_means_ , numeric::functional::plus<array_type const, array_type const>() , numeric::functional::multiply_and_promote_to_double<VariateType const, Weight const>() ); float_type factor = sum * ( (is_same<Impl, relative>::value) ? non_coherent_weighted_tail_mean(args) : 1. ); std::transform( this->tail_means_.begin() , this->tail_means_.end() , this->tail_means_.begin() , std::bind2nd(numeric::functional::divides<typename array_type::value_type const, float_type const>(), factor) ); return make_iterator_range(this->tail_means_); } private: mutable array_type tail_means_; }; } // namespace impl /////////////////////////////////////////////////////////////////////////////// // tag::absolute_weighted_tail_variate_means // tag::relative_weighted_tail_variate_means // namespace tag { template<typename LeftRight, typename VariateType, typename VariateTag> struct absolute_weighted_tail_variate_means : depends_on<non_coherent_weighted_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight>, tail_weights<LeftRight> > { typedef accumulators::impl::weighted_tail_variate_means_impl<mpl::_1, mpl::_2, absolute, LeftRight, VariateType> impl; }; template<typename LeftRight, typename VariateType, typename VariateTag> struct relative_weighted_tail_variate_means : depends_on<non_coherent_weighted_tail_mean<LeftRight>, tail_variate<VariateType, VariateTag, LeftRight>, tail_weights<LeftRight> > { typedef accumulators::impl::weighted_tail_variate_means_impl<mpl::_1, mpl::_2, relative, LeftRight, VariateType> impl; }; } /////////////////////////////////////////////////////////////////////////////// // extract::weighted_tail_variate_means // extract::relative_weighted_tail_variate_means // namespace extract { extractor<tag::abstract_absolute_tail_variate_means> const weighted_tail_variate_means = {}; extractor<tag::abstract_relative_tail_variate_means> const relative_weighted_tail_variate_means = {}; } using extract::weighted_tail_variate_means; using extract::relative_weighted_tail_variate_means; // weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(absolute) -> absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> template<typename LeftRight, typename VariateType, typename VariateTag> struct as_feature<tag::weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(absolute)> { typedef tag::absolute_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type; }; // weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(relative) -> relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> template<typename LeftRight, typename VariateType, typename VariateTag> struct as_feature<tag::weighted_tail_variate_means<LeftRight, VariateType, VariateTag>(relative)> { typedef tag::relative_weighted_tail_variate_means<LeftRight, VariateType, VariateTag> type; }; }} // namespace boost::accumulators #ifdef _MSC_VER # pragma warning(pop) #endif #endif