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Diffstat (limited to 'boost/accumulators/statistics/pot_tail_mean.hpp')
| -rw-r--r-- | boost/accumulators/statistics/pot_tail_mean.hpp | 211 |
1 files changed, 211 insertions, 0 deletions
diff --git a/boost/accumulators/statistics/pot_tail_mean.hpp b/boost/accumulators/statistics/pot_tail_mean.hpp new file mode 100644 index 0000000000..088ef98093 --- /dev/null +++ b/boost/accumulators/statistics/pot_tail_mean.hpp @@ -0,0 +1,211 @@ +/////////////////////////////////////////////////////////////////////////////// +// 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 |