On the max-domain of attractions of bivariate elliptical arrays
Hashorva, Enkelejd
In: Extremes, 2005, vol. 8, no. 3, p. 225-233
Ajouter à la liste personnelle- Summary
- Let $$(U_{ni},V_{ni}), 1 \le i \le n, n\ge 1$$ be a triangular array of independent bivariate elliptical random vectors with the same distribution function as $$\bigl( S_1, \rho_n S_1 + \sqrt{1- \rho_n^2}S_2\bigr), \rho_n \in (0,1)$$ where $$(S_1, S_2)$$ is a bivariate spherical random vector. Under assumptions on the speed of convergence of $$\rho_n\to 1$$ we show in this paper that the maxima of this triangular array is in the max-domain of attraction of a new max-id. distribution function $$H_{\alpha,\lambda}$$ , provided that $$\sqrt{S_1^2+S_2^2}$$ has distribution function in the max-domain of attraction of the Weibull distribution function $$\Psi_\alpha$$