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Multivariate Matrix Mittag--Leffler distributions
Hansjoerg Albrecher, Martin Bladt, Mogens Bladt · 2020-03-24 · via math.PR updates on arXiv.org

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.

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