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NONNEGATIVITY OF COVARIANCES BETWEEN FUNCTIONS OF ORDERED RANDOM VARIABLES

Published online by Cambridge University Press:  22 October 2007

Taizhong Hu ,
Junchao Yao  and
Qingshu Lu
Taizhong Hu
Affiliation:
Department of Statistics and FinanceUniversity of Science and Technology of ChinaHefei, Anhui 230026People's Republic of China E-mail: [email protected]
Junchao Yao
Affiliation:
Department of Statistics and FinanceUniversity of Science and Technology of ChinaHefei, Anhui 230026People's Republic of China E-mail: [email protected]
Qingshu Lu
Affiliation:
Department of Statistics and FinanceUniversity of Science and Technology of ChinaHefei, Anhui 230026People's Republic of China E-mail: [email protected]
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Abstract

In this article we investigate conditions by a unified method under which the covariances of functions of two adjacent ordered random variables are nonnegative. The main structural results are applied to several kinds of ordered random variable, such as delayed record values, continuous and discrete ℓ∞⩽-spherical order statistics, epoch times of mixed Poisson processes, generalized order statistics, discrete weak record values, and epoch times of modified geometric processes. These applications extend the main results for ordinary order statistics in Qi [28] and for usual record values in Nagaraja and Nevzorov [25].

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 21 , Issue 4 , October 2007 , pp. 557 - 577
Copyright
Copyright © Cambridge University Press 2007

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