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Research Article | Open Access

On moment convergence of sample quantiles with application to parameter estimations for Cauchy distribution

School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, China
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Abstract

Under a general condition on continuous probability distributions of some populations, this study establishes that the distributional convergence of sample quantiles implies moment convergence. As an application, we propose a quick and robust consistent estimator for the shape parameter of the Cauchy distribution under large-sample conditions. This estimator achieves over 99% efficiency relative to the maximum likelihood estimator.

Keywords

asymptotically consistent estimatorCauchy distributionconvergence in distributionconvergence of moments
CLC number: 62F10

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AIMS Mathematics
Volume 10 Issue 12,
December 2025
Pages 30942-30967
DOI: 10.3934/math.20251358

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Cite this article:
Wang Y. On moment convergence of sample quantiles with application to parameter estimations for Cauchy distribution. AIMS Mathematics, 2025, 10(12): 30942-30967. https://doi.org/10.3934/math.20251358

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Received: 08 October 2025
Revised: 14 December 2025
Accepted: 22 December 2025
Published: 31 December 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)