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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.

Keywords

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}
}
R2 v1 2026-06-23T14:24:34.783Z