Extremes of Perturbed Bivariate Rayleigh Risks
Keywords:asymptotic independence, Gumbel max-domain of attraction, Hüsler–Reiss distribution, Rayleigh distribution, triangular arrays
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.
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