On pairwise interaction multivariate Pareto models

Abstract: The rich class of multivariate Pareto distributions forms the basis of recently introduced extremal graphical models. However, most existing literature on the topic is focused on the popular parametric family of H\"usler--Reiss distributions. It is shown that the H\"usler--Reiss family is in fact the only continuous multivariate Pareto model that exhibits the structure of a pairwise interaction model, justifying its use in many high-dimensional problems. Along the way, useful insight is obtained concerning a certain class of distributions considered in arXiv:2303.04258, a result of independent interest.