

























Abstract:In this paper, we develop a novel inferential approach based on geometric records for estimating the tail index of heavy-tailed distributions. We construct a maximum likelihood estimator for the Pareto model and establish strong consistency and asymptotic normality, providing also an explicit expression for the asymptotic variance. These results are then extended to a broad class of Pareto-type distributions. The performance of the estimator is assessed via Monte Carlo simulation and compared with classical estimators from the literature. The proposed method is particularly well suited for settings where data arrive sequentially, as it yields smooth estimation trajectories. It is also especially advantageous in applications such as destructive testing, where measuring each item is costly. In this context, the estimator achieves a comparable level of estimation accuracy to Hill's estimator, but with a considerably lower number of fully measured items. An application to the analysis of the distribution of fluctuations of the Dow Jones Industrial Average (DJI) is also presented.
From: Miguel Lafuente [view email]
[v1]
Tue, 28 Apr 2026 19:11:50 UTC (122 KB)
[v2]
Fri, 3 Jul 2026 17:53:03 UTC (114 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。