The Weibull-tail class of distributions is a sub-class of the Gumbel extreme domain of attraction, and it has caught the attention of a number of researchers in the last decade, particularly concerning the estimation of the so-called Weibull-tail coefficient. In this paper, we propose an estimator of this Weibull-tail coefficient when the Weibull-tail distribution of interest is censored from the right by another Weibull-tail distribution: to the best of our knowledge, this is the first one proposed in this context. A corresponding estimator of extreme quantiles is also proposed. In both mild censoring and heavy censoring (in the tail) settings, asymptotic normality of these estimators is proved, and their finite sample behavior is presented via some simulations.

中文翻译：

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存在随机删失的情况下威布尔尾分布的极值估计

Weibull-tail分布是Gumbel极值吸引域的子类，并且在最近十年中引起了许多研究人员的关注，尤其是在所谓的Weibull-tail系数的估计方面。在本文中，当感兴趣的威布尔尾分布由另一个威布尔尾分布从右边审查时，我们提出了一个威布尔尾系数的估计器：据我们所知，这是在这种情况下提出的第一个威布尔尾系数。还提出了极端分位数的相应估计量。在轻度审查和重度审查（在尾部）设置中，证明了这些估计量的渐近正态性，并通过一些模拟给出了它们的有限样本行为。