Doubly stochastic distributions of extreme events

TL;DR

This paper reviews the Metastatistical Extreme Value Distribution (MEVD), a non-asymptotic approach that models extreme events using doubly stochastic distributions, offering advantages over traditional EV theory by utilizing all available data.

Contribution

The paper provides a detailed derivation and analysis of MEVD, demonstrating its generality and inclusion of other recent doubly stochastic methods for extreme value analysis.

Findings

MEVD explicitly models variability in extreme value processes.

It uses all available data for high-quantile inference.

Includes other recent doubly stochastic approaches.

Abstract

The distribution of block maxima of sequences of independent and identically-distributed random variables is used to model extreme values in many disciplines. The traditional extreme value (EV) theory derives a closed-form expression for the distribution of block maxima under asymptotic assumptions, and is generally fitted using annual maxima or excesses over a high threshold, thereby discarding a large fraction of the available observations. The recently-introduced Metastatistical Extreme Value Distribution (MEVD), a non-asymptotic formulation based on doubly stochastic distributions, has been shown to offer several advantages compared to the traditional EV theory. In particular, MEVD explicitly accounts for the variability of the process generating the extreme values, and uses all the available information to perform high-quantile inferences. Here we review the derivation of the MEVD, analyzing its assumptions in detail, and show that its general formulation includes other doubly stochastic approaches to extreme value analysis that have been recently proposed.