Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-18T02:22:21.012Z Has data issue: false hasContentIssue false
  • English
  • Français

Length-Biased Orderings with Applications

Published online by Cambridge University Press:  27 July 2009

Abdulhamid A. Alzaid
Abdulhamid A. Alzaid
Affiliation:
Department of Statistics College of Science King Saud University Riyadh, 11451, Saudi Arabia
Get access Rights & Permissions [Opens in a new window]

Abstract

A new partial ordering generated by the set of star-shaped functions is introduced. This ordering is equivalent to the stochastic comparison of the length-biased distributions which are frequently appropriate for certain natural sampling plans in biometry, reliability, and survival analysis studies. It is shown that the length-biased ordering fits in the framework of stochastic and variatiility orderings. It enjoys many properties similar to those of the stochastic and variability orderings.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 3 , July 1988 , pp. 329 - 341
Copyright
Copyright © Cambridge University Press 1988

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

Gupta, R.C. & Keating, J.P. (1986). Relations for reliability measures under length-biased sampling. Scandinavian Journal of Statistics 13: 49–56.Google Scholar
Marshall, A.W. & Olkin, I. (1979). Inequalities: Theory of majorization and its applications. New York: Academic Press.Google Scholar
Ross, S. (1983). Stochastic processes. New York: John Wiley & Sons, Inc.Google Scholar
Ross, S.M. & Schechner, Z. (1984). Some reliability applications of the variability ordering. Operations Research 32: 679–687.CrossRefGoogle Scholar
Stoyan, D. (1983). Comparison methods for queues and other stochastic models. New York: John Wiley & Sons, Inc.Google Scholar
Whitt, W. (1980). Uniform conditional stochastic order. Journal of Applied Probability 17: 112–123.CrossRefGoogle Scholar
Whitt, W. (1985). Uniform conditional variability ordering of probability distributions. Journal of Applied Probability 22: 619–633.CrossRefGoogle Scholar