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 |
Keywords:
extreme value distribution; Gumbel’s family; regular variation; multivariate extremal distributions; dependence function; Archimedean copula; domains of attraction of Gumbel distributionsCitations:
Zbl 0093.153References:
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