AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home AIMS Mathematics Article
PDF (742 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
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
Show Author Information

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

References

【1】
【1】
 
 
Crossref Google Scholar
AIMS Mathematics
Volume 10 Issue 12,
December 2025
Pages 30942-30967
DOI: 10.3934/math.20251358

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
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

335

Views

2

Downloads

0

Crossref

0

Web of Science

0

Scopus
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)