Extremes of Perturbed Bivariate Rayleigh Risks

Abstract

We establish first an asymptotic expansion for the joint survival function of a bivariate Rayleigh distribution, one of the most popular probabilistic models in engineering. Furthermore, we show that the component-wise maxima of a Hüsler–Reiss triangular array scheme of independent perturbed bivariate Rayleigh risks converges to a bivariate Hüsler–Reiss random vector.

Keywords

• asymptotic independence
• Gumbel max-domain of attraction
• Hüsler–Reiss distribution
• Rayleigh distribution
• triangular arrays