Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T17:00:29.216Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
Deshpande, J. V., Kochar, S. C. and Singh, H. (1986) Aspects of positive ageing. J Appl. Prob. 23, 748–758.Google Scholar
Deshpande, J. V., Singh, H., Bagai, I. and Jain, K. (1990) Some partial orders describing positive ageing. Commun. Statist.-Stock Models. 6, 471–481.Google Scholar
Fagiuoli, E. and Pellerey, F. (1993) New partial orderings and applications. Naval Res. Logist. 40, 829–842.Google Scholar
Fagiuoli, E. and Pellerey, F. (1994) Preservation of certain classes of life distributions under Poisson shock models. J. Appl. Prob. 31, 458–465.CrossRefGoogle Scholar
Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar
Shaked, M. and Shanthikumar, J. G. (1994) Stochastic Orders and their Applications. Academic Press, New York.Google Scholar
Singh, H. (1989) On partial orderings of life distributions. Naval Res. Logist. 36, 103–110.3.0.CO;2-7>CrossRefGoogle Scholar
Stoyan, D. (1983) Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.Google Scholar