Asymptotic Distributions of Order Statistics from Doubly Truncated Cauchy Distribution

Acta Scientiarum Naturalium Universitatis Pekinensis

Asymptotic Distributions of Order Statistics from Doubly Truncated Cauchy Distribution

KUANG Nenghui, CHEN Yong

School of Mathematics and Computing Science, Hunan University of Science and Technology, Xiangtan 411201;

Received:2010-04-14 Online:2011-05-20 Published:2011-05-20

双截尾的Cauchy 分布顺序统计量的渐近分布

匡能晖,陈勇

湖南科技大学数学与计算科学学院,湘潭 411201;

Abstract

Abstract: Let {X_k, 1 ≤k ≤n} be independent and identically distributed random variables, and X_1:n, X_2:n, … , X_n:n their order statistics. When X_k follows doubly truncated Cauchy distribution with parameters A, B(A1:n and X_n:n are obtained. For a fixed integer k> 1, the asymptotic distributions of X_n:n and X_n-k+1:n are also obtained. What’s more, it proves that X_1:n and X_n:n are asymptotically independent.

Key words: doubly truncated Cauchy distribution, order statistic, asymptotic distribution, asymptotically independent

摘要： 设 {X_k, 1 ≤k ≤n}独立同分布, X_1:n, X_2:n, … , X_n:n为其顺序统计量。当 X_k服从参数为 A 和 B(A1:n和X_n:n的渐近分布; 当 k(k>1)固定时,得到X_n:n和X_n-k+1:n的渐近分布; 并且证明其极端顺序统计量X_1:n和X_n:n是渐近独立的。

关键词: 双截尾的Cauchy分布, 顺序统计量, 渐近分布, 渐近独立

CLC Number:

O211

KUANG Nenghui,CHEN Yong. Asymptotic Distributions of Order Statistics from Doubly Truncated Cauchy Distribution[J]. Acta Scientiarum Naturalium Universitatis Pekinensis.

匡能晖,陈勇. 双截尾的Cauchy 分布顺序统计量的渐近分布[J]. 北京大学学报（自然科学版）.

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https://xbna.pku.edu.cn/EN/Y2011/V47/I3/385

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