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Mathematics > Probability

arXiv:1812.04139 (math)
[Submitted on 10 Dec 2018 (v1), last revised 28 Jun 2019 (this version, v2)]

Title:Inhomogeneous phase--type distributions and heavy tails

Authors:Hansjörg Albrecher, Mogens Bladt
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Abstract:We extend the construction principle of phase-type (PH) distributions to allow for inhomogeneous transition rates and show that this naturally leads to direct probabilistic descriptions of certain transformations of PH distributions. In particular, the resulting matrix distributions enable to carry over fitting properties of PH distributions to distributions with heavy tails, providing a general modelling framework for heavy-tail phenomena. We also illustrate the versatility and parsimony of the proposed approach for the modelling of a real-world heavy-tailed fire insurance dataset.
Subjects: Probability (math.PR)
Cite as: arXiv:1812.04139 [math.PR]
  (or arXiv:1812.04139v2 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1812.04139

Submission history

From: Mogens Bladt [view email]
[v1] Mon, 10 Dec 2018 22:39:43 UTC (92 KB)
[v2] Fri, 28 Jun 2019 06:46:18 UTC (92 KB)
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