Multivariate matrix Mittag-Leffler distributions

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.

Automated summary

This study extends the construction principle of multivariate phase-type distributions to establish a class of heavy-tailed multivariate random variables with Marginal distributions of Mittag-Leffler type. These distributions are shown to be dense among all multivariate positive random variables, making them versatile candidates for modeling tail-independent risks in various fields.