双截尾柯西分布顺序统计量的概率性质

数学理论与应用 ›› 2017, Vol. 37 ›› Issue (2): 79-87.

双截尾柯西分布顺序统计量的概率性质

熊雄¹ ，庹恒²

1.湘潭大学数学与计算科学学院,湘潭,411105; 2.中南大学数学与统计学院,长沙,411100

出版日期:2017-06-30 发布日期:2020-09-23
基金资助:
湖南省教育厅科学研究项目(14C1088)

Probability Properties of Order Statistics to Bilaterally Truncated Cauchy Distribution#br#
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Xiong Xiong¹， Tuo Heng²

1.School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,China; 2.School of Mathematics and Statistics,Central South University,Changsha 411000,China

Online:2017-06-30 Published:2020-09-23

摘要/Abstract

摘要： 设 {X_k,1≤k ≤n}独立同分布,服从参数为μ,λ;A,B 的双截尾柯西分布,X_1,n,X_2,n,…,X_n为其顺序统计量.本文给出X_k,n(1≤k ≤n)的密度函数,X_1,n,X_2,n,…,X_n,n的联合密度函数,极端顺序统计量X_1,n和X_n,n的渐近分布以及Xk,n和X_n-k+1,n (k >1)的渐近分布,并证明X_1,n和X_n,n是渐近独立的.

关键词: 双截尾柯西分布, 顺序统计量, 渐近分布, 渐近独立

Abstract:

Let {X_k,1≤k ≤n}be independent and identically distributed random variables with bilaterally truncated Cauchy distribution of parameters μ,λ,A,B,X_1,n,X_2,n,…,X_n,nbe their order statistics.In this paper we obtain the density function of X_k,n,the joint density function of X_1,n,X_2,n,…,X_n,n,the asymptotic distributions of their extreme order statistics X_1,n and X_n,n,and the asymptotic distributions of X_k,n and X_n-k+1,n.We also show that X_1,nand X_n,n is asymptotically independent.

Key words:

Bilaterally truncated Cauchy distribution, Order statistic, Asymptotic distribution, Asymptotical independence

熊雄, 庹恒. 双截尾柯西分布顺序统计量的概率性质[J]. 数学理论与应用, 2017, 37(2): 79-87.

Xiong Xiong, Tuo Heng. Probability Properties of Order Statistics to Bilaterally Truncated Cauchy Distribution#br#

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[J]. Mathematical Theory and Applications, 2017, 37(2): 79-87.