On the max-domain of attractions of bivariate elliptical arrays

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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 \(\Psi_\alpha\).