Multivariate matrix Mittag–Leffler distributions

Hansjörg Albrecher (), Martin Bladt () and Mogens Bladt ()
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Hansjörg Albrecher: University of Lausanne
Martin Bladt: University of Lausanne
Mogens Bladt: University of Copenhagen

Annals of the Institute of Statistical Mathematics, 2021, vol. 73, issue 2, No 6, 369-394

Abstract: 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: Multivariate distribution; Heavy tails; Markov process; Mittag–Leffler distribution; Phase-type; Matrix distribution; Extremes; Laplace transforms (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10463-020-00750-7

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