Models for Exceedances Over High Thresholds

TLDR

The paper investigates modeling the sizes and occurrences of exceedances over high thresholds in extreme value analysis. The authors employ the generalized Pareto distribution, develop estimation and model‑checking procedures for univariate and regression data, and extend the framework to account for seasonality and serial dependence in exceedance point processes. The methods are illustrated on river flow and wave height data, including an application to siting nuclear installations.

Abstract

SUMMARY We discuss the analysis of the extremes of data by modelling the sizes and occurrence of exceedances over high thresholds. The natural distribution for such exceedances, the generalized Pareto distribution, is described and its properties elucidated. Estimation and model-checking procedures for univariate and regression data are developed, and the influence of and information contained in the most extreme observations in a sample are studied. Models for seasonality and serial dependence in the point process of exceedances are described. Sets of data on river flows and wave heights are discussed, and an application to the siting of nuclear installations is described.