@article{Wang2025, 
author = {Yuankang Wang},
title = {On moment convergence of sample quantiles with application to parameter estimations for Cauchy distribution},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {30942-30967},
keywords = {asymptotically consistent estimator, Cauchy distribution, convergence in distribution, convergence of moments},
url = {https://www.sciopen.com/article/10.3934/math.20251358},
doi = {10.3934/math.20251358},
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.}
}