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THE SECOND-ORDER REGULAR VARIATION OF ORDER STATISTICS
Published online by Cambridge University Press: 13 December 2013
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.
- 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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