Probability in the Engineering & Informational Sciences
Random variables -- Mathematical models, Stochastic analysis, Mathematical statistics
Let X1,..., Xn 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 increasing according to hazard rate ordering. In this article, we prove this conjecture in the case of a single-outlier exponential model when all except 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 vector of scale parameters is more dispersed in the sense of majorization.
Khaledi, E. and Kochar, S. (2001). Stochastic properties of spacings in a single-outlier exponential model. Probability in the Engineering and Informational Sciences, 15, pp 401-408.