Multivariate Discrete Generalized Pareto Distributions: Theory, Simulation, and Applications to Dry spells

TL;DR

This paper extends multivariate extreme value theory to discrete data using generalized Pareto distributions, providing new models, simulation methods, and an application to drought analysis in Europe.

Contribution

It introduces multivariate discrete Pareto distributions, expanding extreme value modeling to discrete data with theoretical foundations and practical inference techniques.

Findings

New multivariate discrete Pareto models developed

Simulation and likelihood-free inference methods demonstrated

Application to drought analysis in Europe showcased effectiveness

Abstract

This article extends the multivariate extreme value theory (MEVT) to discrete settings, focusing on the generalized Pareto distribution (GPD) as a foundational tool. The purpose of the study is to enhance the understanding of extreme discrete count data representation, particularly for discrete exceedances over thresholds, defining and using multivariate discrete Pareto distributions (MDGPD). Through theoretical results and illustrative examples, we outline the construction and properties of MDGPDs, providing practical insights into simulation techniques and data fitting approaches using recent likelihood-free inference methods. This framework broadens the toolkit for modeling extreme events, offering robust methodologies for analyzing multivariate discrete data with extreme values. To illustrate its practical relevance, we present an application of this method to drought analysis, addressing a growing concern in Europe.