Stochastic ordering in multivariate extremes

Corradini, Michela and Strokorb, Kirstin ORCID: https://orcid.org/0000-0001-8748-3014 2024. Stochastic ordering in multivariate extremes. Extremes Item availability restricted.

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Abstract

The article considers the multivariate stochastic orders of upper orthants, lower orthants and positive quadrant dependence (PQD) among simple max-stable distributions and their exponent measures. It is shown for each order that it holds for the max-stable distribution if and only if it holds for the corresponding exponent measure. The finding is non-trivial for upper orthants (and hence PQD order). From dimension d ≥ 3 these three orders are not equivalent and a variety of phenomena can occur. However, every simple max-stable distribution PQD-dominates the corresponding independent model and is PQD-dominated by the fully dependent model. Among parametric models the asymmetric Dirichlet family and the H¨usler-Reiß family turn out to be PQD-ordered according to the natural order within their parameter spaces. For the H¨usler-Reiß family this holds true even for the supermodular order.

Item Type:	Article
Date Type:	Published Online
Status:	In Press
Schools:	Mathematics
Publisher:	Springer
ISSN:	1386-1999
Date of First Compliant Deposit:	11 March 2024
Date of Acceptance:	8 March 2024
Last Modified:	03 Apr 2024 00:04
URI:	https://orca.cardiff.ac.uk/id/eprint/167111

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