Matrix Mittag–Leffler distributions and modeling heavy-tailed risks
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Matrix Mittag–Leffler distributions and modeling heavy-tailed risks. / Albrecher, Hansjörg; Bladt, Martin; Bladt, Mogens.
I: Extremes, Bind 23, Nr. 3, 2020, s. 425-450.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Matrix Mittag–Leffler distributions and modeling heavy-tailed risks
AU - Albrecher, Hansjörg
AU - Bladt, Martin
AU - Bladt, Mogens
PY - 2020
Y1 - 2020
N2 - In this paper we define the class of matrix Mittag-Leffler distributions and study some of its properties. We show that it can be interpreted as a particular case of an inhomogeneous phase-type distribution with random scaling factor, and alternatively also as the absorption time of a semi-Markov process with Mittag-Leffler distributed interarrival times. We then identify this class and its power transforms as a remarkably parsimonious and versatile family for the modeling of heavy-tailed risks, which overcomes some disadvantages of other approaches like the problem of threshold selection in extreme value theory. We illustrate this point both on simulated data as well as on a set of real-life MTPL insurance data that were modeled differently in the past.
AB - In this paper we define the class of matrix Mittag-Leffler distributions and study some of its properties. We show that it can be interpreted as a particular case of an inhomogeneous phase-type distribution with random scaling factor, and alternatively also as the absorption time of a semi-Markov process with Mittag-Leffler distributed interarrival times. We then identify this class and its power transforms as a remarkably parsimonious and versatile family for the modeling of heavy-tailed risks, which overcomes some disadvantages of other approaches like the problem of threshold selection in extreme value theory. We illustrate this point both on simulated data as well as on a set of real-life MTPL insurance data that were modeled differently in the past.
KW - 62E10
KW - 62F10)
KW - 62P05 (33E12
KW - 91G05
KW - Heavy tails
KW - Matrix distributions
KW - Mittag-Leffler functions
KW - Phase-type distributions
KW - Random scaling
KW - Risk modeling
UR - http://www.scopus.com/inward/record.url?scp=85085937155&partnerID=8YFLogxK
U2 - 10.1007/s10687-020-00377-0
DO - 10.1007/s10687-020-00377-0
M3 - Journal article
AN - SCOPUS:85085937155
VL - 23
SP - 425
EP - 450
JO - Extremes
JF - Extremes
SN - 1386-1999
IS - 3
ER -
ID: 243064745