Weibull tail estimation via peak-over-threshold under deterministic thresholds

Abstract

This paper investigates the estimation of the Weibull tail coefficient within the framework of extreme value theory, using the Peak-Over-Threshold approach with a deterministic threshold. Based on maximum likelihood estimation, the methodology offers a unified treatment of the shape parameter and the finite right endpoint, while addressing a key challenge in modeling bounded extremes. Theoretical properties such as existence, consistency, and asymptotic normality of the estimators are established. Furthermore, a new log-excess-based estimator for the Weibull tail coefficient is introduced. The performance of the new estimators in small samples is illustrated through simulations, and their effectiveness, robustness, and practical relevance are further confirmed by real-data applications. This dual validation highlights both their solid theoretical foundation and applied significance.