Summary
Denote byH ak-dimensional extreme value distribution with marginal distributionHi(x)=Λ(x)=exp(−e−x),x∈R1. Then it is proved thatH(x)=Λ(x1)...Λ(xk) for anyx=(x1, ...,xk) ∈Rk, if and only if the equation holds forx=(0,...,0). Next some multivariate extensions of the results by Resnick (1971,J. Appl. Probab.,8, 136–156) on tail equivalence and asymptotic distributions of extremes are established.
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References
Billingsley, P. (1968).Convergence of Probability Measures, Wiley, New York.
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Resnick, S. I. (1971). Tail equivalence and its applications,J. Appl. Probab.,8, 136–156.
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Takahashi, R. Some properties of multivariate extreme value distributions and multivariate tail equivalence. Ann Inst Stat Math 39, 637–647 (1987). https://doi.org/10.1007/BF02491496
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DOI: https://doi.org/10.1007/BF02491496