On the Max-Domain of Attraction of Type-III Elliptical Triangular Arrays

Abstract

Let be a triangular array of independent elliptical random vectors in ℝ ^d ,d ≥ 2. In a recent article, we show for the case d = 2 that the bivariate sample maxima of this triangular array is attracted by a max-infinitely divisible bivariate distribution function, provided that the components of the triangular array become asymptotically dependent and further the random radius associated to the elliptical random vectors has distribution function in the Weibull max-domain of attraction.

Keywords:

• Maxima of triangular arrays
• Max-infinitely divisible distribution
• Multivariate elliptical distribution
• Weak convergence
• Weibull max-domain of attraction

Mathematics Subject Classification:

• Primary 60F05
• Secondary 60G70

Acknowledgments

I would like to thank Professor Samuel Kotz for encouraging correspondence and several useful comments and Professor Yutaka Kano for kindly providing Kano (1994).