Multivariate Matrix Mittag--Leffler distributions

TL;DR

This paper introduces a new class of multivariate heavy-tailed distributions with Mittag-Leffler marginals, extending phase-type distributions by making scalar parameters matrix-valued, useful for modeling tail-independent risks.

Contribution

It develops an analytically tractable multivariate distribution class with Mittag-Leffler marginals, generalizing phase-type distributions through matrix-valued parameters.

Findings

Distribution class is dense among multivariate positive variables

Provides a versatile model for tail-independent heavy-tailed risks

Extends phase-type distribution construction to multivariate case

Abstract

We extend the construction principle of multivariate phase-type distributions to establish an analytically tractable class of heavy-tailed multivariate random variables whose marginal distributions are of Mittag-Leffler type with arbitrary index of regular variation. The construction can essentially be seen as allowing a scalar parameter to become matrix-valued. The class of distributions is shown to be dense among all multivariate positive random variables and hence provides a versatile candidate for the modelling of heavy-tailed, but tail-independent, risks in various fields of application.