boost/accumulators/statistics/weighted_peaks_over_threshold.hpp
/////////////////////////////////////////////////////////////////////////////// // weighted_peaks_over_threshold.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_WEIGHTED_PEAKS_OVER_THRESHOLD_HPP_DE_01_01_2006 #define BOOST_ACCUMULATORS_STATISTICS_WEIGHTED_PEAKS_OVER_THRESHOLD_HPP_DE_01_01_2006 #include <vector> #include <limits> #include <numeric> #include <functional> #include <boost/range.hpp> #include <boost/mpl/if.hpp> #include <boost/mpl/placeholders.hpp> #include <boost/parameter/keyword.hpp> #include <boost/tuple/tuple.hpp> #include <boost/accumulators/numeric/functional.hpp> #include <boost/accumulators/framework/accumulator_base.hpp> #include <boost/accumulators/framework/extractor.hpp> #include <boost/accumulators/framework/parameters/sample.hpp> #include <boost/accumulators/framework/depends_on.hpp> #include <boost/accumulators/statistics_fwd.hpp> #include <boost/accumulators/statistics/parameters/quantile_probability.hpp> #include <boost/accumulators/statistics/peaks_over_threshold.hpp> // for named parameters pot_threshold_value and pot_threshold_probability #include <boost/accumulators/statistics/sum.hpp> #include <boost/accumulators/statistics/tail_variate.hpp> #ifdef _MSC_VER # pragma warning(push) # pragma warning(disable: 4127) // conditional expression is constant #endif namespace boost { namespace accumulators { namespace impl { /////////////////////////////////////////////////////////////////////////////// // weighted_peaks_over_threshold_impl // works with an explicit threshold value and does not depend on order statistics of weighted samples /** @brief Weighted Peaks over Threshold Method for Weighted Quantile and Weighted Tail Mean Estimation @sa peaks_over_threshold_impl @param quantile_probability @param pot_threshold_value */ template<typename Sample, typename Weight, typename LeftRight> struct weighted_peaks_over_threshold_impl : accumulator_base { typedef typename numeric::functional::multiplies<Weight, Sample>::result_type weighted_sample; typedef typename numeric::functional::average<weighted_sample, std::size_t>::result_type float_type; // for boost::result_of typedef boost::tuple<float_type, float_type, float_type> result_type; template<typename Args> weighted_peaks_over_threshold_impl(Args const &args) : sign_((is_same<LeftRight, left>::value) ? -1 : 1) , mu_(sign_ * numeric::average(args[sample | Sample()], (std::size_t)1)) , sigma2_(numeric::average(args[sample | Sample()], (std::size_t)1)) , w_sum_(numeric::average(args[weight | Weight()], (std::size_t)1)) , threshold_(sign_ * args[pot_threshold_value]) , fit_parameters_(boost::make_tuple(0., 0., 0.)) , is_dirty_(true) { } template<typename Args> void operator ()(Args const &args) { this->is_dirty_ = true; if (this->sign_ * args[sample] > this->threshold_) { this->mu_ += args[weight] * args[sample]; this->sigma2_ += args[weight] * args[sample] * args[sample]; this->w_sum_ += args[weight]; } } template<typename Args> result_type result(Args const &args) const { if (this->is_dirty_) { this->is_dirty_ = false; this->mu_ = this->sign_ * numeric::average(this->mu_, this->w_sum_); this->sigma2_ = numeric::average(this->sigma2_, this->w_sum_); this->sigma2_ -= this->mu_ * this->mu_; float_type threshold_probability = numeric::average(sum_of_weights(args) - this->w_sum_, sum_of_weights(args)); float_type tmp = numeric::average(( this->mu_ - this->threshold_ )*( this->mu_ - this->threshold_ ), this->sigma2_); float_type xi_hat = 0.5 * ( 1. - tmp ); float_type beta_hat = 0.5 * ( this->mu_ - this->threshold_ ) * ( 1. + tmp ); float_type beta_bar = beta_hat * std::pow(1. - threshold_probability, xi_hat); float_type u_bar = this->threshold_ - beta_bar * ( std::pow(1. - threshold_probability, -xi_hat) - 1.)/xi_hat; this->fit_parameters_ = boost::make_tuple(u_bar, beta_bar, xi_hat); } return this->fit_parameters_; } private: short sign_; // for left tail fitting, mirror the extreme values mutable float_type mu_; // mean of samples above threshold mutable float_type sigma2_; // variance of samples above threshold mutable float_type w_sum_; // sum of weights of samples above threshold float_type threshold_; mutable result_type fit_parameters_; // boost::tuple that stores fit parameters mutable bool is_dirty_; }; /////////////////////////////////////////////////////////////////////////////// // weighted_peaks_over_threshold_prob_impl // determines threshold from a given threshold probability using order statistics /** @brief Peaks over Threshold Method for Quantile and Tail Mean Estimation @sa weighted_peaks_over_threshold_impl @param quantile_probability @param pot_threshold_probability */ template<typename Sample, typename Weight, typename LeftRight> struct weighted_peaks_over_threshold_prob_impl : accumulator_base { typedef typename numeric::functional::multiplies<Weight, Sample>::result_type weighted_sample; typedef typename numeric::functional::average<weighted_sample, std::size_t>::result_type float_type; // for boost::result_of typedef boost::tuple<float_type, float_type, float_type> result_type; template<typename Args> weighted_peaks_over_threshold_prob_impl(Args const &args) : sign_((is_same<LeftRight, left>::value) ? -1 : 1) , mu_(sign_ * numeric::average(args[sample | Sample()], (std::size_t)1)) , sigma2_(numeric::average(args[sample | Sample()], (std::size_t)1)) , threshold_probability_(args[pot_threshold_probability]) , fit_parameters_(boost::make_tuple(0., 0., 0.)) , is_dirty_(true) { } void operator ()(dont_care) { this->is_dirty_ = true; } template<typename Args> result_type result(Args const &args) const { if (this->is_dirty_) { this->is_dirty_ = false; float_type threshold = sum_of_weights(args) * ( ( is_same<LeftRight, left>::value ) ? this->threshold_probability_ : 1. - this->threshold_probability_ ); std::size_t n = 0; Weight sum = Weight(0); while (sum < threshold) { if (n < static_cast<std::size_t>(tail_weights(args).size())) { mu_ += *(tail_weights(args).begin() + n) * *(tail(args).begin() + n); sigma2_ += *(tail_weights(args).begin() + n) * *(tail(args).begin() + n) * (*(tail(args).begin() + n)); sum += *(tail_weights(args).begin() + n); n++; } else { if (std::numeric_limits<float_type>::has_quiet_NaN) { return boost::make_tuple( std::numeric_limits<float_type>::quiet_NaN() , std::numeric_limits<float_type>::quiet_NaN() , std::numeric_limits<float_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 boost::make_tuple(Sample(0), Sample(0), Sample(0)); } } } float_type u = *(tail(args).begin() + n - 1) * this->sign_; this->mu_ = this->sign_ * numeric::average(this->mu_, sum); this->sigma2_ = numeric::average(this->sigma2_, sum); this->sigma2_ -= this->mu_ * this->mu_; if (is_same<LeftRight, left>::value) this->threshold_probability_ = 1. - this->threshold_probability_; float_type tmp = numeric::average(( this->mu_ - u )*( this->mu_ - u ), this->sigma2_); float_type xi_hat = 0.5 * ( 1. - tmp ); float_type beta_hat = 0.5 * ( this->mu_ - u ) * ( 1. + tmp ); float_type beta_bar = beta_hat * std::pow(1. - threshold_probability_, xi_hat); float_type u_bar = u - beta_bar * ( std::pow(1. - threshold_probability_, -xi_hat) - 1.)/xi_hat; this->fit_parameters_ = boost::make_tuple(u_bar, beta_bar, xi_hat); } return this->fit_parameters_; } private: short sign_; // for left tail fitting, mirror the extreme values mutable float_type mu_; // mean of samples above threshold u mutable float_type sigma2_; // variance of samples above threshold u mutable float_type threshold_probability_; mutable result_type fit_parameters_; // boost::tuple that stores fit parameters mutable bool is_dirty_; }; } // namespace impl /////////////////////////////////////////////////////////////////////////////// // tag::weighted_peaks_over_threshold // namespace tag { template<typename LeftRight> struct weighted_peaks_over_threshold : depends_on<sum_of_weights> , pot_threshold_value { /// INTERNAL ONLY typedef accumulators::impl::weighted_peaks_over_threshold_impl<mpl::_1, mpl::_2, LeftRight> impl; }; template<typename LeftRight> struct weighted_peaks_over_threshold_prob : depends_on<sum_of_weights, tail_weights<LeftRight> > , pot_threshold_probability { /// INTERNAL ONLY typedef accumulators::impl::weighted_peaks_over_threshold_prob_impl<mpl::_1, mpl::_2, LeftRight> impl; }; } /////////////////////////////////////////////////////////////////////////////// // extract::weighted_peaks_over_threshold // namespace extract { extractor<tag::abstract_peaks_over_threshold> const weighted_peaks_over_threshold = {}; } using extract::weighted_peaks_over_threshold; // weighted_peaks_over_threshold<LeftRight>(with_threshold_value) -> weighted_peaks_over_threshold<LeftRight> template<typename LeftRight> struct as_feature<tag::weighted_peaks_over_threshold<LeftRight>(with_threshold_value)> { typedef tag::weighted_peaks_over_threshold<LeftRight> type; }; // weighted_peaks_over_threshold<LeftRight>(with_threshold_probability) -> weighted_peaks_over_threshold_prob<LeftRight> template<typename LeftRight> struct as_feature<tag::weighted_peaks_over_threshold<LeftRight>(with_threshold_probability)> { typedef tag::weighted_peaks_over_threshold_prob<LeftRight> type; }; }} // namespace boost::accumulators #ifdef _MSC_VER # pragma warning(pop) #endif #endif