Multivariate matrix Mittag–Leffler distributions

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Standard

Multivariate matrix Mittag–Leffler distributions. / Albrecher, Hansjörg; Bladt, Martin; Bladt, Mogens.

I: Annals of the Institute of Statistical Mathematics, Bind 73, Nr. 2, 2021, s. 369 - 394.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Albrecher, H, Bladt, M & Bladt, M 2021, 'Multivariate matrix Mittag–Leffler distributions', Annals of the Institute of Statistical Mathematics, bind 73, nr. 2, s. 369 - 394. https://doi.org/10.1007/s10463-020-00750-7

APA

Albrecher, H., Bladt, M., & Bladt, M. (2021). Multivariate matrix Mittag–Leffler distributions. Annals of the Institute of Statistical Mathematics, 73(2), 369 - 394. https://doi.org/10.1007/s10463-020-00750-7

Vancouver

Albrecher H, Bladt M, Bladt M. Multivariate matrix Mittag–Leffler distributions. Annals of the Institute of Statistical Mathematics. 2021;73(2):369 - 394. https://doi.org/10.1007/s10463-020-00750-7

Author

Albrecher, Hansjörg ; Bladt, Martin ; Bladt, Mogens. / Multivariate matrix Mittag–Leffler distributions. I: Annals of the Institute of Statistical Mathematics. 2021 ; Bind 73, Nr. 2. s. 369 - 394.

Bibtex

@article{101b9f761014459e9a0453253f8b088d,
title = "Multivariate matrix Mittag–Leffler distributions",
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 = "Extremes, Heavy tails, Laplace transforms, Markov process, Matrix distribution, Mittag–Leffler distribution, Multivariate distribution, Phase-type",
author = "Hansj{\"o}rg Albrecher and Martin Bladt and Mogens Bladt",
year = "2021",
doi = "10.1007/s10463-020-00750-7",
language = "English",
volume = "73",
pages = "369 -- 394",
journal = "Annals of the Institute of Statistical Mathematics",
issn = "0020-3157",
publisher = "Springer",
number = "2",

}

RIS

TY - JOUR

T1 - Multivariate matrix Mittag–Leffler distributions

AU - Albrecher, Hansjörg

AU - Bladt, Martin

AU - Bladt, Mogens

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Extremes

KW - Heavy tails

KW - Laplace transforms

KW - Markov process

KW - Matrix distribution

KW - Mittag–Leffler distribution

KW - Multivariate distribution

KW - Phase-type

UR - http://www.scopus.com/inward/record.url?scp=85082933517&partnerID=8YFLogxK

U2 - 10.1007/s10463-020-00750-7

DO - 10.1007/s10463-020-00750-7

M3 - Journal article

AN - SCOPUS:85082933517

VL - 73

SP - 369

EP - 394

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

SN - 0020-3157

IS - 2

ER -

ID: 243007552