# Multivariate generalized Pareto distributions: parametrizations, representations, and properties

## TL;DR

This paper provides a comprehensive overview of multivariate generalized Pareto distributions, detailing their parametrizations, representations, and stability properties, serving as a practical guide for researchers working with these distributions.

## Contribution

It introduces multiple parametrizations and representations of multivariate generalized Pareto distributions, highlighting their stability properties and offering a useful reference for applications.

## Key findings

- Multiple parametrizations facilitate flexible modeling.
- Distributions exhibit notable stability properties.
- The paper consolidates key features for practical use.

## Abstract

Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized and represented in a number of different ways. Moreover, generalized Pareto distributions enjoy a number of interesting stability properties. An overview of the main features of such distributions are given, expressed compactly in several parametrizations, giving the potential user of these distributions a convenient catalogue of ways to handle and work with generalized Pareto distributions.