An Intuitive Curve-Fit Approach to Probability-Preserving Prediction of Extremes

TL;DR

This paper introduces a simple, intuitive curve-fitting method for predicting extreme values beyond historical data, which preserves probability accurately and is applicable to various distributions.

Contribution

It presents a novel, probability-preserving curve-fit approach based on the double-logarithmic QQ-plot for predicting extremes beyond observed data.

Findings

Method accurately predicts extreme values outside data range

Applicable to a wide class of distributions including GPD

Preserves probability with good approximation

Abstract

A method is described for predicting extremes values beyond the span of historical data. The method - based on extending a curve fitted to a location- and scale-invariant variation of the double-logarithmic QQ-plot - is simple and intuitive, yet it preserves probability to a good approximation. The procedure is developed on the Generalised Pareto Distribution (GPD), but is applicable to the upper order statistics of a wide class of distributions.