#### Published In

Probability in the Engineering & Informational Sciences

#### Document Type

Article

#### Publication Date

10-1-2000

#### Subjects

Random variables -- Mathematical models, Stochastic analysis, Mathematical statistics

#### Abstract

In this paper, we study the dependence properties of spacings. It is proved that if X_{1},..., X_{n} are exchangeable random variables which are TP_{2} in pairs and their joint density is log-convex in each argument, then the spacings are MTP_{2} 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 MTP_{2} dependent. However, in the case of a single outlier when all except one parameters are equal, the spacings are shown to be MTP_{2} 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 TP_{2} dependent.

#### Persistent Identifier

http://archives.pdx.edu/ds/psu/9520

#### Citation Details

Khaledi, E. and Kochar, S. (2000). Dependence among spacings. Probability in the Engineering and Informational Sciences, 14, pp 461-472.

## Description

This is the publisher's final PDF. Article appears in Probability in the Engineering and Informational Sciences (http://journals.cambridge.org/action/displayJournal?jid=PES) and is Copyright © 2000 Cambridge University Press.