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Multivariate matrix Mittag–Leffler distributions

Author

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  • Hansjörg Albrecher

    (University of Lausanne)

  • Martin Bladt

    (University of Lausanne)

  • Mogens Bladt

    (University of Copenhagen)

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.

Suggested Citation

  • Hansjörg Albrecher & Martin Bladt & Mogens Bladt, 2021. "Multivariate matrix Mittag–Leffler distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(2), pages 369-394, April.
    • Handle: RePEc:spr:aistmt:v:73:y:2021:i:2:d:10.1007_s10463-020-00750-7
    DOI: 10.1007/s10463-020-00750-7
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    References listed on IDEAS

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    5. Anderson, Dale N., 1992. "A multivariate Linnik distribution," Statistics & Probability Letters, Elsevier, vol. 14(4), pages 333-336, July.
    6. Harry Joe & Haijun Li, 2011. "Tail Risk of Multivariate Regular Variation," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 671-693, December.
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