Multivariate matrix Mittag–Leffler distributions
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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
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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