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DEPENDENCE AMONG SPACINGS

Published online by Cambridge University Press:  31 October 2000

Baha-Eldin Khaledi  and
Subhash Kochar
Baha-Eldin Khaledi
Affiliation:
Indian Statistical Institute, New Delhi-110016, India
Subhash Kochar
Affiliation:
Indian Statistical Institute, New Delhi-110016, India, E-mail: [email protected]
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Abstract

In this paper, we study the dependence properties of spacings. It is proved that if X1,..., Xn are exchangeable random variables which are TP2 in pairs and their joint density is log-convex in each argument, then the spacings are MTP2 dependent. Next, we consider the case of independent but nonhomogeneous exponential random variables. It is shown that in this case, in general, the spacings are not MTP2 dependent. However, in the case of a single outlier when all except one parameters are equal, the spacings are shown to be MTP2 dependent and, hence, they are associated. A consequence of this result is that in this case, the variances of the order statistics are increasing. It is also proved that in the case of the multiple-outliers model, all consecutive pairs of spacings are TP2 dependent.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 14 , Issue 4 , October 2000 , pp. 461 - 472
Copyright
© 2000 Cambridge University Press

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