Stochastic properties of spacings in a single-outlier exponential model

Let X-1,..., X-n be independent exponential random variables with possibly different scale parameters. Kochar and Korwar [J. Multivar. Anal. 57 (1996) ] conjectured that, in this case, the successive normalized spacings are in creasing according to hazard rate ordering. In this article, we prove this conjecture in the case of a single-outlier exponential model when all excep t one of the parameters are identical. We also prove that the spacings are more dispersed and larger in the sense of hazard rate ordering when the vec tor of scale parameters is more dispersed in the sense of majorization.