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