Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-19T10:50:57.707Z Has data issue: false hasContentIssue false
  • English
  • Français

Laplace Transform Characterization of Probabilistic Orderings

Published online by Cambridge University Press:  27 July 2009

Y. Kebir
Y. Kebir
Affiliation:
Department of Management Science and Mathematical Sciences, Loyola University of Chicago, Chicago, Illinois 60611
Get access Rights & Permissions [Opens in a new window]

Abstract

Using the Laplace transform, we characterize, by means of necessary and sufficient conditions, the property that two life distributions are ordered in the sense of stochastic ordering, hazard rate ordering, backward hazard rate ordering, and likelihood ratio ordering.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 8 , Issue 1 , January 1994 , pp. 69 - 77
Copyright
Copyright © Cambridge University Press 1994

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

1.A-Hameed, M.S. & Proschan, F. (1973). Non-stationary shock models. Stochastic Processes and Their Applications 1: 383–404.CrossRefGoogle Scholar
2.Barlow, R.E. & Proschan, F. (1981). Statistical theory of reliability and life testing. Silver Spring, MD: To Begin With.Google Scholar
3.Block, H.W. & Savits, T. (1980). Laplace transform for classes of life distributions. Annals of Probability 8: 465–474.CrossRefGoogle Scholar
4.Esary, J.D., Marshall, A.W., & Proschan, F. (1973). Shock models and wear processes. Annals of Probability 1: 627–649.CrossRefGoogle Scholar
5.Feller, W. (1971). An introduction to probability theory and its applications. Vol. 2. New York: John Wiley.Google Scholar
6.Karlin, S. (1968). Total positivity, Vol. 1. Stanford, CA: Stanford University Press.Google Scholar
7.Keilson, J. & Sumita, U. (1982). Uniform stochastic ordering and related inequalities. Canadian Journal of Statistics 10: 181–198.CrossRefGoogle Scholar
8.Klefsjo, B. (1982). The HNBUE and HNWUE classes of life distributions. Naval Research Logistics 29: 331–344.CrossRefGoogle Scholar
9.Ross, S.M. (1983). Stochastic processes. New York: John Wiley.Google Scholar
10.Stoyan, D. (1983). Comparison methods for queues and other stochastic models. New York: John Wiley.Google Scholar
11.Vinogradov, O.P. (1973). The definition of distribution functions with increasing hazard rate in terms of the Laplace transform. Theory of Probability and Its Applications 18: 811–814.CrossRefGoogle Scholar