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211 lines
7.4 KiB
211 lines
7.4 KiB
/////////////////////////////////////////////////////////////////////////////// |
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// pot_tail_mean.hpp |
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// |
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// Copyright 2006 Daniel Egloff, Olivier Gygi. Distributed under the Boost |
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// Software License, Version 1.0. (See accompanying file |
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) |
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#ifndef BOOST_ACCUMULATORS_STATISTICS_POT_TAIL_MEAN_HPP_DE_01_01_2006 |
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#define BOOST_ACCUMULATORS_STATISTICS_POT_TAIL_MEAN_HPP_DE_01_01_2006 |
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#include <vector> |
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#include <limits> |
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#include <numeric> |
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#include <functional> |
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#include <boost/range.hpp> |
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#include <boost/parameter/keyword.hpp> |
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#include <boost/tuple/tuple.hpp> |
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#include <boost/mpl/if.hpp> |
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#include <boost/mpl/placeholders.hpp> |
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#include <boost/type_traits/is_same.hpp> |
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#include <boost/accumulators/framework/accumulator_base.hpp> |
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#include <boost/accumulators/framework/extractor.hpp> |
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#include <boost/accumulators/numeric/functional.hpp> |
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#include <boost/accumulators/framework/parameters/sample.hpp> |
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#include <boost/accumulators/statistics_fwd.hpp> |
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#include <boost/accumulators/statistics/peaks_over_threshold.hpp> |
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#include <boost/accumulators/statistics/weighted_peaks_over_threshold.hpp> |
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#include <boost/accumulators/statistics/pot_quantile.hpp> |
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#include <boost/accumulators/statistics/tail_mean.hpp> |
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namespace boost { namespace accumulators |
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{ |
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namespace impl |
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{ |
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/////////////////////////////////////////////////////////////////////////////// |
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// pot_tail_mean_impl |
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// |
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/** |
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@brief Estimation of the (coherent) tail mean based on the peaks over threshold method (for both left and right tails) |
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Computes an estimate for the (coherent) tail mean |
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\f[ |
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\widehat{CTM}_{\alpha} = \hat{q}_{\alpha} - \frac{\bar{\beta}}{\xi-1}(1-\alpha)^{-\xi}, |
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\f] |
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where \f$\bar[u]\f$, \f$\bar{\beta}\f$ and \f$\xi\f$ are the parameters of the |
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generalized Pareto distribution that approximates the right tail of the distribution (or the |
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mirrored left tail, in case the left tail is used). In the latter case, the result is mirrored |
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back, yielding the correct result. |
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*/ |
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template<typename Sample, typename Impl, typename LeftRight> |
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struct pot_tail_mean_impl |
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: accumulator_base |
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{ |
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typedef typename numeric::functional::average<Sample, std::size_t>::result_type float_type; |
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// for boost::result_of |
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typedef float_type result_type; |
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pot_tail_mean_impl(dont_care) |
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: sign_((is_same<LeftRight, left>::value) ? -1 : 1) |
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{ |
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} |
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template<typename Args> |
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result_type result(Args const &args) const |
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{ |
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typedef |
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typename mpl::if_< |
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is_same<Impl, weighted> |
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, tag::weighted_peaks_over_threshold<LeftRight> |
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, tag::peaks_over_threshold<LeftRight> |
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>::type |
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peaks_over_threshold_tag; |
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typedef |
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typename mpl::if_< |
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is_same<Impl, weighted> |
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, tag::weighted_pot_quantile<LeftRight> |
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, tag::pot_quantile<LeftRight> |
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>::type |
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pot_quantile_tag; |
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extractor<peaks_over_threshold_tag> const some_peaks_over_threshold = {}; |
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extractor<pot_quantile_tag> const some_pot_quantile = {}; |
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float_type beta_bar = some_peaks_over_threshold(args).template get<1>(); |
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float_type xi_hat = some_peaks_over_threshold(args).template get<2>(); |
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return some_pot_quantile(args) - this->sign_ * beta_bar/( xi_hat - 1. ) * std::pow( |
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is_same<LeftRight, left>::value ? args[quantile_probability] : 1. - args[quantile_probability] |
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, -xi_hat); |
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} |
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private: |
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short sign_; // if the fit parameters from the mirrored left tail extreme values are used, mirror back the result |
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}; |
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} // namespace impl |
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/////////////////////////////////////////////////////////////////////////////// |
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// tag::pot_tail_mean |
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// tag::pot_tail_mean_prob |
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// |
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namespace tag |
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{ |
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template<typename LeftRight> |
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struct pot_tail_mean |
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: depends_on<peaks_over_threshold<LeftRight>, pot_quantile<LeftRight> > |
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{ |
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/// INTERNAL ONLY |
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/// |
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typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, unweighted, LeftRight> impl; |
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}; |
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template<typename LeftRight> |
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struct pot_tail_mean_prob |
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: depends_on<peaks_over_threshold_prob<LeftRight>, pot_quantile_prob<LeftRight> > |
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{ |
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/// INTERNAL ONLY |
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/// |
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typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, unweighted, LeftRight> impl; |
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}; |
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template<typename LeftRight> |
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struct weighted_pot_tail_mean |
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: depends_on<weighted_peaks_over_threshold<LeftRight>, weighted_pot_quantile<LeftRight> > |
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{ |
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/// INTERNAL ONLY |
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/// |
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typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, weighted, LeftRight> impl; |
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}; |
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template<typename LeftRight> |
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struct weighted_pot_tail_mean_prob |
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: depends_on<weighted_peaks_over_threshold_prob<LeftRight>, weighted_pot_quantile_prob<LeftRight> > |
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{ |
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/// INTERNAL ONLY |
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/// |
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typedef accumulators::impl::pot_tail_mean_impl<mpl::_1, weighted, LeftRight> impl; |
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}; |
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} |
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// pot_tail_mean<LeftRight>(with_threshold_value) -> pot_tail_mean<LeftRight> |
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template<typename LeftRight> |
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struct as_feature<tag::pot_tail_mean<LeftRight>(with_threshold_value)> |
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{ |
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typedef tag::pot_tail_mean<LeftRight> type; |
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}; |
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// pot_tail_mean<LeftRight>(with_threshold_probability) -> pot_tail_mean_prob<LeftRight> |
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template<typename LeftRight> |
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struct as_feature<tag::pot_tail_mean<LeftRight>(with_threshold_probability)> |
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{ |
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typedef tag::pot_tail_mean_prob<LeftRight> type; |
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}; |
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// weighted_pot_tail_mean<LeftRight>(with_threshold_value) -> weighted_pot_tail_mean<LeftRight> |
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template<typename LeftRight> |
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struct as_feature<tag::weighted_pot_tail_mean<LeftRight>(with_threshold_value)> |
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{ |
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typedef tag::weighted_pot_tail_mean<LeftRight> type; |
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}; |
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// weighted_pot_tail_mean<LeftRight>(with_threshold_probability) -> weighted_pot_tail_mean_prob<LeftRight> |
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template<typename LeftRight> |
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struct as_feature<tag::weighted_pot_tail_mean<LeftRight>(with_threshold_probability)> |
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{ |
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typedef tag::weighted_pot_tail_mean_prob<LeftRight> type; |
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}; |
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// for the purposes of feature-based dependency resolution, |
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// pot_tail_mean<LeftRight> and pot_tail_mean_prob<LeftRight> provide |
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// the same feature as tail_mean |
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template<typename LeftRight> |
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struct feature_of<tag::pot_tail_mean<LeftRight> > |
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: feature_of<tag::tail_mean> |
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{ |
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}; |
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template<typename LeftRight> |
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struct feature_of<tag::pot_tail_mean_prob<LeftRight> > |
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: feature_of<tag::tail_mean> |
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{ |
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}; |
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// So that pot_tail_mean can be automatically substituted |
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// with weighted_pot_tail_mean when the weight parameter is non-void. |
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template<typename LeftRight> |
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struct as_weighted_feature<tag::pot_tail_mean<LeftRight> > |
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{ |
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typedef tag::weighted_pot_tail_mean<LeftRight> type; |
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}; |
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template<typename LeftRight> |
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struct feature_of<tag::weighted_pot_tail_mean<LeftRight> > |
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: feature_of<tag::pot_tail_mean<LeftRight> > |
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{ |
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}; |
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// So that pot_tail_mean_prob can be automatically substituted |
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// with weighted_pot_tail_mean_prob when the weight parameter is non-void. |
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template<typename LeftRight> |
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struct as_weighted_feature<tag::pot_tail_mean_prob<LeftRight> > |
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{ |
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typedef tag::weighted_pot_tail_mean_prob<LeftRight> type; |
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}; |
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template<typename LeftRight> |
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struct feature_of<tag::weighted_pot_tail_mean_prob<LeftRight> > |
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: feature_of<tag::pot_tail_mean_prob<LeftRight> > |
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{ |
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}; |
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}} // namespace boost::accumulators |
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#endif
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