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THE SECOND-ORDER REGULAR VARIATION OF ORDER STATISTICS

Published online by Cambridge University Press:  13 December 2013

Qing Liu ,
Tiantian Mao  and
Taizhong Hu
Qing Liu
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China. E-mails: qliu8310@mail.ustc.edu.cn; tmao@ustc.edu.cn; thu@ustc.edu.cn
Tiantian Mao
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China. E-mails: qliu8310@mail.ustc.edu.cn; tmao@ustc.edu.cn; thu@ustc.edu.cn
Taizhong Hu
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China. E-mails: qliu8310@mail.ustc.edu.cn; tmao@ustc.edu.cn; thu@ustc.edu.cn
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Abstract

Let X1, …, Xn be non-negative, independent and identically distributed random variables with a common distribution function F, and denote by X1:n ≤ ··· ≤ Xn:n the corresponding order statistics. In this paper, we investigate the second-order regular variation (2RV) of the tail probabilities of Xk:n and Xj:n − Xi:n under the assumption that $\bar {F}$ is of the 2RV, where 1 ≤ k ≤ n and 1 ≤ i < j ≤ n.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 28 , Issue 2 , April 2014 , pp. 209 - 222
Copyright
Copyright © Cambridge University Press 2013 

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