/////////////////////////////////////////////////////////////////////////////// | |
// 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 |