| /////////////////////////////////////////////////////////////////////////////// |
| // 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 = {}; |
| |
| BOOST_ACCUMULATORS_IGNORE_GLOBAL(weighted_tail_variate_means) |
| BOOST_ACCUMULATORS_IGNORE_GLOBAL(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 |