Dependence, Dispersiveness, And Multivariate Hazard Rate Ordering

Authors:
Baha-Eldin Khaledi;Subhash Kochar
Affiliations:
Statistical Research Center, Tehran, Iran, and, Department of Statistics, College of Sciences, Razi University, Kermanshah, Iran, E-mail: bkhaledi@hotmail.com;Department of Mathematics and Statistics, Portland State University, Portland, Oregon 97201, E-mail: subhash.kochar@gmail.com
Venue:
Probability in the Engineering and Informational Sciences
Year:
2005

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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.