arXiv subjects

Z. Weng

Publications and source records attributed to Z. Weng.

3 recordsLinked to original sources

arXiv2014

Limit Laws for Extremes of Dependent Stationary Gaussian Arrays

In this paper we show that the componentwise maxima ofweakly dependent bivariate stationary Gaussian triangular arrays converge in distribution after normalisation to Hüsler-Reiss distribution. Under a strong dependence assumption, we prove that the limit distribution of the maxima is a mixture of a bivariate Gaussian distribution and Hüsler-Reiss distribution. Another finding of our paper is that the componentwise maxima and componentwise minima remain asymptotically independent even in the settings of Hüsler and Reiss (1989) allowing further for weak dependence. Further we derive an almost sure limit theorem under the Berman condition for the components of the triangular array.

math.PR↗

arXiv2014

Tail asymptotic of Weibull-type risks

In this paper we derive the tail asymptotics of the product of two dependent Weibull-type risks, which is of interest in various statistical and applied probability problems. Our results extend some recent findings of Schlueter and Fischer (2012) and Bose et al. (2012).

math.PR↗

arXiv2014

Higher-order expansions of distributions of maxima in a Hüsler-Reiss model

The max-stable Hüsler-Reiss distribution which arises as the limit distribution of maxima of bivariate Gaussian triangular arrays has been shown to be useful in various extreme value models. For such triangular arrays, this paper establishes higher-order asymptotic expansions of the joint distribution of maxima under refined Hüsler-Reiss conditions. In particular, the rate of convergence of normalized maxima to the Hüsler-Reiss distribution is explicitly calculated.

math.PR↗