Some properties of multivariate extreme value distributions and multivariate tail equivalence

Summary Denote byH ak-dimensional extreme value distribution with marginal distributionH _i (x)=Λ(x)=exp(−e ^−x ),x∈R ¹. Then it is proved thatH(x)=Λ(x ₁)...Λ(x _k ) for anyx=(x ₁, ...,x _k ) ∈R ^k , 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.