STOCHASTIC PROPERTIES OF SPACINGS IN A SINGLE-OUTLIER EXPONENTIAL MODEL

Authors:
Baha-Eldin Khaledi;Subhash Kochar
Affiliations:
Department of Mathematics, University of Arizona, Tucson, Arizona 85721, E-mail: bkhaledi@math.arizona.edu;Indian Statistical Institute, New Delhi, 110016, India, E-mail: kochar@.isid.ac.in
Venue:
Probability in the Engineering and Informational Sciences
Year:
2001

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Abstract

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.