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 = {};
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