| /////////////////////////////////////////////////////////////////////////////// |
| // pot_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_POT_TAIL_MEAN_HPP_DE_01_01_2006 |
| #define BOOST_ACCUMULATORS_STATISTICS_POT_TAIL_MEAN_HPP_DE_01_01_2006 |
| |
| #include <vector> |
| #include <limits> |
| #include <numeric> |
| #include <functional> |
| #include <boost/range.hpp> |
| #include <boost/parameter/keyword.hpp> |
| #include <boost/tuple/tuple.hpp> |
| #include <boost/mpl/if.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/peaks_over_threshold.hpp> |
| #include <boost/accumulators/statistics/weighted_peaks_over_threshold.hpp> |
| #include <boost/accumulators/statistics/pot_quantile.hpp> |
| #include <boost/accumulators/statistics/tail_mean.hpp> |
| |
| namespace boost { namespace accumulators |
| { |
| |
| namespace impl |
| { |
| /////////////////////////////////////////////////////////////////////////////// |
| // pot_tail_mean_impl |
| // |
| /** |
| @brief Estimation of the (coherent) tail mean based on the peaks over threshold method (for both left and right tails) |
| |
| Computes an estimate for the (coherent) tail mean |
| \f[ |
| \widehat{CTM}_{\alpha} = \hat{q}_{\alpha} - \frac{\bar{\beta}}{\xi-1}(1-\alpha)^{-\xi}, |
| \f] |
| where \f$\bar[u]\f$, \f$\bar{\beta}\f$ and \f$\xi\f$ are the parameters of the |
| generalized Pareto distribution that approximates the right tail of the distribution (or the |
| mirrored left tail, in case the left tail is used). In the latter case, the result is mirrored |
| back, yielding the correct result. |
| */ |
| template<typename Sample, typename Impl, typename LeftRight> |
| struct pot_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; |
| |
| pot_tail_mean_impl(dont_care) |
| : sign_((is_same<LeftRight, left>::value) ? -1 : 1) |
| { |
| } |
| |
| template<typename Args> |
| result_type result(Args const &args) const |
| { |
| typedef |
| typename mpl::if_< |
| is_same<Impl, weighted> |
| , tag::weighted_peaks_over_threshold<LeftRight> |
| , tag::peaks_over_threshold<LeftRight> |
| >::type |
| peaks_over_threshold_tag; |
| |
| typedef |
| typename mpl::if_< |
| is_same<Impl, weighted> |
| , tag::weighted_pot_quantile<LeftRight> |
| , tag::pot_quantile<LeftRight> |
| >::type |
| pot_quantile_tag; |
| |
| extractor<peaks_over_threshold_tag> const some_peaks_over_threshold = {}; |
| extractor<pot_quantile_tag> const some_pot_quantile = {}; |
| |
| float_type beta_bar = some_peaks_over_threshold(args).template get<1>(); |
| float_type xi_hat = some_peaks_over_threshold(args).template get<2>(); |
| |
| return some_pot_quantile(args) - this->sign_ * beta_bar/( xi_hat - 1. ) * std::pow( |
| is_same<LeftRight, left>::value ? args[quantile_probability] : 1. - args[quantile_probability] |
| , -xi_hat); |
| } |
| private: |
| short sign_; // if the fit parameters from the mirrored left tail extreme values are used, mirror back the result |
| }; |
| } // namespace impl |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| // tag::pot_tail_mean |
| // tag::pot_tail_mean_prob |
| // |
| namespace tag |
| { |
| template<typename LeftRight> |
| struct pot_tail_mean |
| : depends_on<peaks_over_threshold<LeftRight>, pot_quantile<LeftRight> > |
| { |
| /// INTERNAL ONLY |
| /// |
| typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, unweighted, LeftRight> impl; |
| }; |
| template<typename LeftRight> |
| struct pot_tail_mean_prob |
| : depends_on<peaks_over_threshold_prob<LeftRight>, pot_quantile_prob<LeftRight> > |
| { |
| /// INTERNAL ONLY |
| /// |
| typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, unweighted, LeftRight> impl; |
| }; |
| template<typename LeftRight> |
| struct weighted_pot_tail_mean |
| : depends_on<weighted_peaks_over_threshold<LeftRight>, weighted_pot_quantile<LeftRight> > |
| { |
| /// INTERNAL ONLY |
| /// |
| typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, weighted, LeftRight> impl; |
| }; |
| template<typename LeftRight> |
| struct weighted_pot_tail_mean_prob |
| : depends_on<weighted_peaks_over_threshold_prob<LeftRight>, weighted_pot_quantile_prob<LeftRight> > |
| { |
| /// INTERNAL ONLY |
| /// |
| typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, weighted, LeftRight> impl; |
| }; |
| } |
| |
| // pot_tail_mean<LeftRight>(with_threshold_value) -> pot_tail_mean<LeftRight> |
| template<typename LeftRight> |
| struct as_feature<tag::pot_tail_mean<LeftRight>(with_threshold_value)> |
| { |
| typedef tag::pot_tail_mean<LeftRight> type; |
| }; |
| |
| // pot_tail_mean<LeftRight>(with_threshold_probability) -> pot_tail_mean_prob<LeftRight> |
| template<typename LeftRight> |
| struct as_feature<tag::pot_tail_mean<LeftRight>(with_threshold_probability)> |
| { |
| typedef tag::pot_tail_mean_prob<LeftRight> type; |
| }; |
| |
| // weighted_pot_tail_mean<LeftRight>(with_threshold_value) -> weighted_pot_tail_mean<LeftRight> |
| template<typename LeftRight> |
| struct as_feature<tag::weighted_pot_tail_mean<LeftRight>(with_threshold_value)> |
| { |
| typedef tag::weighted_pot_tail_mean<LeftRight> type; |
| }; |
| |
| // weighted_pot_tail_mean<LeftRight>(with_threshold_probability) -> weighted_pot_tail_mean_prob<LeftRight> |
| template<typename LeftRight> |
| struct as_feature<tag::weighted_pot_tail_mean<LeftRight>(with_threshold_probability)> |
| { |
| typedef tag::weighted_pot_tail_mean_prob<LeftRight> type; |
| }; |
| |
| // for the purposes of feature-based dependency resolution, |
| // pot_tail_mean<LeftRight> and pot_tail_mean_prob<LeftRight> provide |
| // the same feature as tail_mean |
| template<typename LeftRight> |
| struct feature_of<tag::pot_tail_mean<LeftRight> > |
| : feature_of<tag::tail_mean> |
| { |
| }; |
| |
| template<typename LeftRight> |
| struct feature_of<tag::pot_tail_mean_prob<LeftRight> > |
| : feature_of<tag::tail_mean> |
| { |
| }; |
| |
| // So that pot_tail_mean can be automatically substituted |
| // with weighted_pot_tail_mean when the weight parameter is non-void. |
| template<typename LeftRight> |
| struct as_weighted_feature<tag::pot_tail_mean<LeftRight> > |
| { |
| typedef tag::weighted_pot_tail_mean<LeftRight> type; |
| }; |
| |
| template<typename LeftRight> |
| struct feature_of<tag::weighted_pot_tail_mean<LeftRight> > |
| : feature_of<tag::pot_tail_mean<LeftRight> > |
| { |
| }; |
| |
| // So that pot_tail_mean_prob can be automatically substituted |
| // with weighted_pot_tail_mean_prob when the weight parameter is non-void. |
| template<typename LeftRight> |
| struct as_weighted_feature<tag::pot_tail_mean_prob<LeftRight> > |
| { |
| typedef tag::weighted_pot_tail_mean_prob<LeftRight> type; |
| }; |
| |
| template<typename LeftRight> |
| struct feature_of<tag::weighted_pot_tail_mean_prob<LeftRight> > |
| : feature_of<tag::pot_tail_mean_prob<LeftRight> > |
| { |
| }; |
| |
| }} // namespace boost::accumulators |
| |
| #endif |