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A characterization of Gumbel’s family of extreme value distributions. (English) Zbl 0701.62060

Summary: A family of multivariate extremal distributions proposed by E. J. Gumbel [Publ. Inst. Statist. Univ. Paris 9, 171-173 (1960; Zbl 0093.153)] is characterized among those whose dependence function is an Archimedean copula. The domains of attraction of Gumbel distributions are also determined within this class.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62E10 Characterization and structure theory of statistical distributions

Citations:

Zbl 0093.153
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References:

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