| /////////////////////////////////////////////////////////////////////////////// |
| // 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 = {}; |
| |
| BOOST_ACCUMULATORS_IGNORE_GLOBAL(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 |