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DEPENDENCE, DISPERSIVENESS, AND MULTIVARIATE HAZARD RATE ORDERING

Published online by Cambridge University Press:  31 August 2005

Baha-Eldin Khaledi  and
Subhash Kochar
Baha-Eldin Khaledi
Affiliation:
Statistical Research Center, Tehran, Iran, and, Department of Statistics, College of Sciences, Razi University, Kermanshah, Iran, E-mail: bkhaledi@hotmail.com
Subhash Kochar
Affiliation:
Department of Mathematics and Statistics, Portland State University, Portland, Oregon 97201, E-mail: subhash.kochar@gmail.com
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Abstract

To compare two multivariate random vectors of the same dimension, we define a new stochastic order called upper orthant dispersive ordering and study its properties. We study its relationship with positive dependence and multivariate hazard rate ordering as defined by Hu, Khaledi, and Shaked (Journal of Multivariate Analysis, 2002). It is shown that if two random vectors have a common copula and if their marginal distributions are ordered according to dispersive ordering in the same direction, then the two random vectors are ordered according to this new upper orthant dispersive ordering. Also, it is shown that the marginal distributions of two upper orthant dispersive ordered random vectors are also dispersive ordered. Examples and applications are given.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 19 , Issue 4 , October 2005 , pp. 427 - 446
Copyright
© 2005 Cambridge University Press

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