Multivariate matrix Mittag–Leffler distributions
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- MULTIVARIATE MATRIX MITTAG–LEFFLER DISTRIBUTIONS
Accepted author manuscript, 5.44 MB, PDF document
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.
Original language | English |
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Journal | Annals of the Institute of Statistical Mathematics |
Volume | 73 |
Issue number | 2 |
Pages (from-to) | 369 - 394 |
ISSN | 0020-3157 |
DOIs | |
Publication status | Published - 2021 |
- Extremes, Heavy tails, Laplace transforms, Markov process, Matrix distribution, Mittag–Leffler distribution, Multivariate distribution, Phase-type
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