Max-stable models for multivariate extremes

TL;DR

This paper reviews max-stable models for multivariate extremes, discusses their descriptions, and introduces a construction device for generating parametric families, enhancing modeling capabilities in multivariate extreme-value analysis.

Contribution

It provides a comprehensive overview of max-stable models and proposes a construction device for creating new parametric families, expanding the toolkit for multivariate extreme-value modeling.

Findings

Detailed descriptions of max-stable models

Introduction of a construction device for parametric families

Potential for improved multivariate extreme-value modeling

Abstract

Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theory suggests the use of max-stable models for univariate and multivariate extremes. A comprehensive account is given of the various ways in which max-stable models are described. Furthermore, a construction device is proposed for generating parametric families of max-stable distributions. Although the device is not new, its role as a model generator seems not yet to have been fully exploited.