Stochastic orders for spacings of heterogeneous exponential random variables
Journal of Multivariate Analysis
Positive Dependence Properties of Conditionally Independent Random Lifetimes
Mathematics of Operations Research
STOCHASTIC PROPERTIES OF SPACINGS IN A SINGLE-OUTLIER EXPONENTIAL MODEL
Probability in the Engineering and Informational Sciences
Negative dependence in the balls and bins experiment with applications to order statistics
Journal of Multivariate Analysis
Tp2 dependence of sample spacings with applications
Probability in the Engineering and Informational Sciences
Multivariate dependence of spacings of generalized order statistics
Journal of Multivariate Analysis
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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.