极值次序统计量的联合极限分布

数学物理学报 ›› 2026, Vol. 46 ›› Issue (1): 286-304.

极值次序统计量的联合极限分布

陶颖¹(), 彭作祥²(), 谭中权¹^,^*()

¹嘉兴大学数据科学学院浙江嘉兴 314001
²西南大学数学与统计学院重庆 400715

收稿日期:2025-06-18 修回日期:2025-07-19 出版日期:2026-02-26 发布日期:2026-01-19
通讯作者: 谭中权 E-mail:tywy12@126.com;pzx@swu.edu.cn;tzq728@zjxu.edu.cn
作者简介:陶颖, Email: tywy12@126.com;
彭作祥, Email: pzx@swu.edu.cn
基金资助:
嘉兴市级公益性研究专项(2025CGZ014);"创新嘉兴$\cdot$优才支持计划"拔尖人才

The Joint Limiting Distribution of the Upper and the Lower Extreme Order Statistics with Random Sample Size

Ying Tao¹(), Zuoxiang Peng²(), Zhongquan Tan¹^,^*()

¹College of Data Science, Jiaxing University, Zhejiang Jiaxing 314001
²School of Mathematics and Statistics, Southwest University, Chongqing 400715

Received:2025-06-18 Revised:2025-07-19 Online:2026-02-26 Published:2026-01-19
Contact: Zhongquan Tan E-mail:tywy12@126.com;pzx@swu.edu.cn;tzq728@zjxu.edu.cn
Supported by:
Jiaxing Public Welfare Program Research Project(2025CGZ014);"Innovation Jiaxing $\cdot$ Elite Talent Support Program" Top Talent Project

摘要/Abstract

摘要：

受文献 Vasudeva (Metrika, 2024, 87: 571-584) 启发, 该文研究了随机样本容量情形下上极值次序统计量与下极值次序统计量的联合极限分布. 设 $\{X_{n}, n\geq1\}$ 为一列平稳随机变量, $N(n)$ 是一列取值为正整数值的随机变量. 首先, 该文获得了最大值 $M_{N(n)} =\max\left \{X_{1},X_{2}, \cdots,X_{N(n)} \right \}$ 与最小值 $W_{N(n)} =\min\left \{ X_{1},X_{2}, \cdots,X_{N(n)} \right \}$ 的联合极限分布; 其次, 该文将上述结果推广到了随机样本容量情形下上极值次序统计量与下极值次序统计量联合情形, 所得结论推广了文献 Vasudeva (Metrika, 2024, 87: 571-584) 的主要结论.

关键词: 平稳序列, 上极值次序统计量, 下极值次序统计量, 随机样本容量.}

Abstract:

Motivated by the paper of Vasudeva (Metrika, 2024, 87: 571-584), this paper studied the joint limiting distribution of the upper and the lower extreme order statistics with random sample size. Let $\{X_{n}, n\geq1\}$ be a sequence of random variables and $N(n)$ be a sequence of positive integer random variables. Under some conditions, we derive first the joint limiting distribution of $M_{N(n)} =\max\left \{X_{1}, X_{2}, \cdots, X_{N(n)} \right \}$ and $W_{N(n)} =\min\left \{ X_{1}, X_{2}, \cdots, X_{N(n)} \right \}$ and then we extended the result to the case of the upper and the lower extreme order statistics. The obtained results extended that of Vasudeva (Metrika, 2024, 87: 571-584).

Key words: stationary sequence, the upper extreme order statistics, the lower extreme order statistics, random sample size

陶颖, 彭作祥, 谭中权. 极值次序统计量的联合极限分布[J]. 数学物理学报, 2026, 46(1): 286-304.

Ying Tao, Zuoxiang Peng, Zhongquan Tan. The Joint Limiting Distribution of the Upper and the Lower Extreme Order Statistics with Random Sample Size[J]. Acta mathematica scientia,Series A, 2026, 46(1): 286-304.

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