Struct template peaks_over_threshold_implboost::accumulators::impl::peaks_over_threshold_impl — Peaks over Threshold Method for Quantile and Tail Mean Estimation. Synopsistemplate<typename Sample, typename LeftRight> struct peaks_over_threshold_impl { // types typedef numeric::functional::average< Sample, std::size_t >::result_type float_type; typedef boost::tuple< float_type, float_type, float_type > result_type; typedef mpl::int_< is_same< LeftRight, left >::value?1:1 > sign; // construct/copy/destruct template<typename Args> peaks_over_threshold_impl(Args const &); // public member functions template<typename Args> void operator()(Args const &) ; template<typename Args> result_type result(Args const &) const; }; DescriptionAccording to the theorem of PickandsBalkemade Haan, the distribution function of the excesses over some sufficiently high threshold of a distribution function may be approximated by a generalized Pareto distribution
Note that in case extreme values of the left tail are fitted, the distribution is mirrored with respect to the axis such that the left tail can be treated as a right tail. The computed fit parameters thus define the Pareto distribution that fits the mirrored left tail. When quantities like a quantile or a tail mean are computed using the fit parameters obtained from the mirrored data, the result is mirrored back, yielding the correct result. For further details, see J. R. M. Hosking and J. R. Wallis, Parameter and quantile estimation for the generalized Pareto distribution, Technometrics, Volume 29, 1987, p. 339349 A. J. McNeil and R. Frey, Estimation of TailRelated Risk Measures for Heteroscedastic Financial Time Series: an Extreme Value Approach, Journal of Empirical Finance, Volume 7, 2000, p. 271300
