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.


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


Zbl 0093.153
Full Text: DOI


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