Multivariate Matrix Mittag--Leffler distributions

2020/03/23 by Albrecher, Hansjoerg, Bladt, Martin, Bladt, Mogens · 1 citation
#FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2003.10517

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.

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• Statistics of Extremes for the Insurance Industry

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