In this paper, we revisit the construction of confidence intervals for extreme quantiles of Pareto‐type distributions. A novel asymptotic pivotal quantity is proposed for these quantile estimators, which leads to new asymptotic confidence intervals that exhibit more accurate coverage probability. This pivotal quantity also allows for the construction of a saddle‐point approximation, from which a second set of new confidence intervals follows. The small‐sample properties and utility of these confidence intervals are studied using simulations and a case study from insurance.

中文翻译：

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极端帕累托型分位数的置信区间

在本文中，我们重新审视了帕累托型分布的极端分位数的置信区间的构建。为这些分位数估计量提出了一种新的渐近关键量，这会导致新的渐近置信区间表现出更准确的覆盖概率。这个关键量还允许构建鞍点近似值，从中可以得出第二组新的置信区间。使用模拟和保险案例研究来研究这些置信区间的小样本特性和效用。