The paper deals with the asymptotic laws of functionals of standard exponential random variables. These classes of statistics are closely related to estimators of the extreme value index when the underlying distribution function is in theWeibull domain of attraction.We use techniques based on martingales theory to describe the non-Gaussian asymptotic distribution of the aforementioned statistics.We provide results of a simulation study as well as statistical tests that may be of interest with the proposed results.

中文翻译：

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一个超级mart论论证，用于表征小参数的希尔函数弱定律

本文讨论了标准指数随机变量泛函的渐近律。当基础分布函数在吸引力的威布尔域中时，这些统计量类别与极值指数的估计值密切相关。我们使用基于mar理论的技术来描述上述统计量的非高斯渐近分布。模拟研究以及统计测试可能对建议的结果感兴趣。