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STOCHASTIC PROPERTIES OF SPACINGS IN A SINGLE-OUTLIER EXPONENTIAL MODEL

Published online by Cambridge University Press:  27 July 2001

Baha-Eldin Khaledi  and
Subhash Kochar
Baha-Eldin Khaledi
Affiliation:
Department of Mathematics, University of Arizona, Tucson, Arizona 85721, E-mail: bkhaledi@math.arizona.edu
Subhash Kochar
Affiliation:
Indian Statistical Institute, New Delhi, 110016, India, E-mail: kochar@.isid.ac.in
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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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 15 , Issue 3 , July 2001 , pp. 401 - 408
Copyright
© 2001 Cambridge University Press

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