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Inequalities for the extremal coefficients of multivariate extreme value distributions.

Research output: Contribution to journalJournal article

Published

Journal publication date03/2002
JournalExtremes
Journal number1
Volume5
Number of pages16
Pages87-102
Original languageEnglish

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.