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Estimating the tail index of Pareto-type distributions fr...
[Submitted on 28 Apr 2026 (v1), last revised 3 Jul 2026 (this ve · 2026-04-29 · via stat updates on arXiv.org

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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.

Submission history

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)

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