Acta Scientiarum Naturalium Universitatis Pekinensis

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Asymptotic Distributions of Order Statistics from Doubly Truncated Cauchy Distribution

KUANG Nenghui, CHEN Yong   

  1. 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


  1. 湖南科技大学数学与计算科学学院,湘潭 411201;

Abstract: Let {Xk, 1 ≤k ≤n} be independent and identically distributed random variables, and X1:n, X2:n, … , Xn:n their order statistics. When Xk follows doubly truncated Cauchy distribution with parameters A, B(A1:n and Xn:n are obtained. For a fixed integer k> 1, the asymptotic distributions of Xn:n and Xn-k+1:n are also obtained. What’s more, it proves that X1:n and Xn:n are asymptotically independent.

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

摘要: 设 {Xk, 1 ≤k ≤n}独立同分布, X1:n, X2:n, … , Xn:n为其顺序统计量。当 Xk服从参数为 A 和 B(A1:n和Xn:n的渐近分布; 当 k(k>1)固定时,得到Xn:n和Xn-k+1:n的渐近分布; 并且证明其极端顺序统计量X1:n和Xn: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

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