| /////////////////////////////////////////////////////////////////////////////// |
| // 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::average<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::average(quantile(args), n) |
| * ( |
| ( is_same<LeftRight, left>::value ) ? args[quantile_probability] : 1. - args[quantile_probability] |
| - numeric::average(n, count(args)) |
| ); |
| } |
| }; |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| // 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::average<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::average( |
| 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); |
| } |
| } |
| } |
| }; |
| |
| } // 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 |