Heavy-tailed phase-type distributions: a unified approach.

Bladt, Martin; Yslas, Jorge (2022). Heavy-tailed phase-type distributions: a unified approach. Extremes, 25(3), pp. 529-565. Springer 10.1007/s10687-022-00436-8

[img]
Preview
Text
Bladt-Yslas2022_Article_Heavy-tailedPhase-typeDistribu.pdf - Published Version
Available under License Creative Commons: Attribution (CC-BY).

Download (5MB) | Preview

A phase-type distribution is the distribution of the time until absorption in a finite state-space time-homogeneous Markov jump process, with one absorbing state and the rest being transient. These distributions are mathematically tractable and conceptually attractive to model physical phenomena due to their interpretation in terms of a hidden Markov structure. Three recent extensions of regular phase-type distributions give rise to models which allow for heavy tails: discrete- or continuous-scaling; fractional-time semi-Markov extensions; and inhomogeneous time-change of the underlying Markov process. In this paper, we present a unifying theory for heavy-tailed phase-type distributions for which all three approaches are particular cases. Our main objective is to provide useful models for heavy-tailed phase-type distributions, but any other tail behavior is also captured by our specification. We provide relevant new examples and also show how existing approaches are naturally embedded. Subsequently, two multivariate extensions are presented, inspired by the univariate construction which can be considered as a matrix version of a frailty model. We provide fully explicit EM-algorithms for all models and illustrate them using synthetic and real-life data.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Yslas Altamirano, Jorge

Subjects:

300 Social sciences, sociology & anthropology > 360 Social problems & social services
500 Science > 510 Mathematics

ISSN:

1386-1999

Publisher:

Springer

Language:

English

Submitter:

Pubmed Import

Date Deposited:

29 Jul 2022 16:07

Last Modified:

05 Dec 2022 16:22

Publisher DOI:

10.1007/s10687-022-00436-8

PubMed ID:

35899174

Uncontrolled Keywords:

Frailty models Heavy tails Parameter estimation Phase-type Scale mixtures

BORIS DOI:

10.48350/171637

URI:

https://boris.unibe.ch/id/eprint/171637

Actions (login required)

Edit item Edit item
Provide Feedback