Second-order refined peaks-over-threshold modelling for heavy-tailed distributions

TL;DR

This paper introduces an extended peaks-over-threshold model that accurately describes excesses over lower thresholds in heavy-tailed distributions, allowing for more data to be modeled and more stable tail parameter estimates.

Contribution

It proposes a second-order refined model extending the generalized Pareto distribution for better threshold flexibility in heavy-tailed data.

Findings

Model fits well for lower thresholds in heavy-tailed data

Tail parameter estimates are more stable across thresholds

Supported by asymptotic analysis, simulations, and a case study

Abstract

Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typically requires high thresholds in order for the (G)PD to fit well and in such a case applies only to a small upper fraction of the data. The extension of the (G)PD proposed in this paper is able to describe the excess distribution for lower thresholds in case of heavy tailed distributions. This yields a statistical model that can be fitted to a larger portion of the data. Moreover, estimates of tail parameters display stability for a larger range of thresholds. Our findings are supported by asymptotic results, simulations and a case study.