Stochastic properties of spacings in a single-outlier exponential model (Q2748556)

Let \(X_1,X_2,\dots, X_n\) be independent exponential random variables with possibly different scale parameters. \textit{S. C. Kochar} and \textit{R. Korwar} conjectured [J. Multivariate Anal. 57, No. 1, 69-83 (1996; Zbl 0864.62032)] that, in this case, the successive normalized spacings are increasing, according to the hazard rate ordering. The aim of the present article is to prove this conjecture in the case of a single-outlier exponential model, when all except one of the parameters are identical. Furthermore, the spacings are proved to be more dispersed and larger, in the sense of hazard rate ordering, when the vector of scale parameters is more dispersed in the sense of majorization ordering.