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Extreme value attractors for star unimodal copulas. (English) Zbl 0996.60026

This work examines the maximum domain of attraction for star unimodal copulas. For copulas that are star unimodal about \((a,b) \neq (1,1)\) the maximum domain is an element of a two-parameter family of copulas extending that of Cuadras-Auge. When \((a,b) = (1,1)\) the set of all possible attractors covers all maximum (extreme) values of star unimodality. Also, the archimax copulas of Ph. Capéraà, A.-L. Fougères and C. Genest [J. Multivariate Anal. 72, No. 1, 30-49 (2000; Zbl 0978.62043)] are studied. Many of the last copulas are not star unimodal.

MSC:

60E99 Distribution theory
62H05 Characterization and structure theory for multivariate probability distributions; copulas

Citations:

Zbl 0978.62043
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Full Text: DOI

References:

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