极值次序统计量的联合极限分布

Abstract

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

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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References 34

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

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