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Inequalities for the extremal coefficients of multivariate extreme value distributions.

Schlather, Martin and Tawn, Jonathan A. (2002) Inequalities for the extremal coefficients of multivariate extreme value distributions. Extremes, 5 (1). pp. 87-102. ISSN 1386-1999

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Abstract

The extremal coefficients are the natural dependence measures for multivariate extreme value distributions. For an m-variate distribution 2m distinct extremal coefficients of different orders exist; they are closely linked and therefore a complete set of 2m coefficients cannot take any arbitrary values. We give a full characterization of all the sets of extremal coefficients. To this end, we introduce a simple class of extreme value distributions that allows for a 1-1 mapping to the complete sets of extremal coefficients. We construct bounds that higher order extremal coefficients need to satisfy to be consistent with lower order extremal coefficients. These bounds are useful as lower order extremal coefficients are the most easily inferred from data.

Item Type: Article
Journal or Publication Title: Extremes
Uncontrolled Keywords: dependence measures - extremal coefficient - multivariate extreme value distribution - inequalities - self-consistency
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 19293
Deposited By: ep_ss_importer
Deposited On: 18 Nov 2008 16:35
Refereed?: Yes
Published?: Published
Last Modified: 09 Oct 2013 15:40
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/19293

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