Orthogonal parametrisations of Extreme-Value distributions

TL;DR

This paper introduces orthogonal reparametrisations of key extreme-value distributions to improve inference stability and interpretability, especially when fitting small samples in risk assessment applications.

Contribution

It applies Cox and Reid's theory to develop orthogonal parametrisations for GEV, GPD, and Gumbel distributions, enhancing modeling of rare events.

Findings

Orthogonal reparametrisations improve inference stability.

Simulation shows better estimation properties.

Enhanced interpretability of parameters.

Abstract

Extreme value distributions are routinely employed to assess risks connected to extreme events in a large number of applications. They typically are two- or three- parameter distributions: the inference can be unstable, which is particularly problematic given the fact that often times these distributions are fitted to small samples. Furthermore, the distribution's parameters are generally not directly interpretable and not the key aim of the estimation. We present several orthogonal reparametrisations of the main extreme-value distributions, key in the modelling of rare events. In particular, we apply the theory developed in Cox and Reid (1987) to the Generalised Extreme-Value, Generalised Pareto, and Gumbel distributions. We illustrate the principal advantage of these reparametrisations in a simulation study.