Extreme behavior of multivariate phase-type distributions

Asimit, A.V. & Jones, B. (2007). Extreme behavior of multivariate phase-type distributions. Insurance: Mathematics and Economics, 41(2), pp. 223-233. doi: 10.1016/j.insmatheco.2006.10.016

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Abstract

This paper investigates the limiting distributions of the componentwise maxima and minima of suitably normalized iid multivariate phase-type random vectors. In the case of maxima, a large parametric class of multivariate extreme value (MEV) distributions is obtained. The flexibility of this new class is exemplified in the bivariate setup. For minima, it is shown that the dependence structure of the Marshall-Olkin class arises in the limit.

Item Type:	Article
Additional Information:	© 2007, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Uncontrolled Keywords:	Componentwise maxima (minima); Copula; Marshall–Olkin exponential distribution; Multivariate extreme value distribution; Pickands’ representation
Subjects:	H Social Sciences > HG Finance Q Science > QA Mathematics
Divisions:	Cass Business School > Faculty of Actuarial Science & Insurance
Related URLs:	https://ssrn.com/abstract=2323550
URI:	http://openaccess.city.ac.uk/id/eprint/13144

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