高斯分布的极差中值与极差的渐近性

数学物理学报 ›› 2026, Vol. 46 ›› Issue (3): 1183-1193.

高斯分布的极差中值与极差的渐近性

唐广¹(), 鲁盈吟¹^,^*(), 喻婷婷²()

¹ 西南石油大学理学院成都 610500
² 西南石油大学教务部四川南充 637001

收稿日期:2025-03-17 修回日期:2026-01-19 出版日期:2026-06-26 发布日期:2026-06-16
通讯作者: 鲁盈吟 E-mail:hhdtt1314@163.com;luyingyin93@163.com;ytt8624@163.com
作者简介:唐广, E-mail:hhdtt1314@163.com;
喻婷婷, E-mail:ytt8624@163.com
基金资助:
南充市哲学社会科学研究与规划项目(NC23C194)

Asymptotics of Sample Median Range and Sample Range from Gaussian Distribution

Guang Tang¹(), Yingyin Lu¹^,^*(), Tingting Yu²()

¹ School of Sciences, Southwest Petroleum University, Chengdu 610500
² Department of Academic Affairs, Southwest Petroleum University, Sichuan Nanchong 637001

Received:2025-03-17 Revised:2026-01-19 Online:2026-06-26 Published:2026-06-16
Contact: Yingyin Lu E-mail:hhdtt1314@163.com;luyingyin93@163.com;ytt8624@163.com
Supported by:
Research and Planning Project of Nanchong City on Philosophy and Social Science(NC23C194)

摘要/Abstract

摘要：

该文研究了高斯分布的规范化样本极差中值和样本极差的极限分布, 并在相同的规范化常数下建立了它们的高阶渐近分布展开式. 进一步推导并证明了这两个规范化分布收敛至其极限分布时具有相同的收敛速率. 此外, 数值分析结果也验证并支持了该结论.

关键词: 高斯分布, 极差中值, 极差, 高阶渐近分布展开式.

Abstract:

In this paper, we investigate the limiting distributions of the normalized sample median range and sample range from Gaussian distributions. Additionally, the distributional expansions are established with the same normalizing constants. A byproduct is to deduce the convergence rates of the distributions of the normalized sample median range and sample range to their limits, which shows they have the same convergence rate. Furthermore, numerical analysis is provided to illustrate the theoretical findings.

Key words: Gaussian distribution, sample median range, sample range, distributional expansion.

中图分类号:

O212.2

唐广, 鲁盈吟, 喻婷婷. 高斯分布的极差中值与极差的渐近性[J]. 数学物理学报, 2026, 46(3): 1183-1193.

Guang Tang, Yingyin Lu, Tingting Yu. Asymptotics of Sample Median Range and Sample Range from Gaussian Distribution[J]. Acta mathematica scientia,Series A, 2026, 46(3): 1183-1193.

图/表 4

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