Multivariate Matrix Mittag--Leffler distributions
Probability
2020-03-25 v1 Statistics Theory
Statistics Theory
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.
Cite
@article{arxiv.2003.10517,
title = {Multivariate Matrix Mittag--Leffler distributions},
author = {Hansjoerg Albrecher and Martin Bladt and Mogens Bladt},
journal= {arXiv preprint arXiv:2003.10517},
year = {2020}
}