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On closure of some partial orderings under mixtures

Part of: Distribution theory - Probability Special processes

Published online by Cambridge University Press:  14 July 2016

Asok K. Nanda ,
Kanchan Jain  and
Harshinder Singh
Asok K. Nanda*
Affiliation:
Panjab University
Kanchan Jain*
Affiliation:
Panjab University
Harshinder Singh*
Affiliation:
Panjab University
*
∗Postal address for all authors: Department of Statistics, Panjab University, Chandigarh-160014, India.
∗Postal address for all authors: Department of Statistics, Panjab University, Chandigarh-160014, India.
∗Postal address for all authors: Department of Statistics, Panjab University, Chandigarh-160014, India.
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Abstract

Recently new partial orderings s-SFR, s-FR, s-ST, s-CV and s-CX have been defined in the literature. These are more general in the sense that most of the earlier known partial orderings reduce to particular cases of these orderings. Moreover, these orderings have helped in defining a new and useful ageing criterion. In this paper, we discuss preservation properties of these orderings under mixtures. Results are expected to be useful in engineering and reliability, where mixtures of distributions arise naturally in numerous situations. Moreover, existing results, specifically for LR, FR and ST orderings under the operation of mixtures, reduce to special cases.

Keywords

EQUILIBRIUM DISTRIBUTIONSMIXTURE OF DISTRIBUTIONSPARTIAL ORDERINGS

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 60E15: Inequalities; stochastic orderings
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 3 , September 1996 , pp. 698 - 706
Copyright
Copyright © Applied Probability Trust 1996 

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