Skip to main content
SpringerLink
Log in

Preservation properties for the mean residual life ordering

  • Articles
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

Sereral preservation results for the mean residual life (mr) ordering are given. In particular, we show that the mr-ordering is preserved under convolutions, mixtures and weak convergence.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alzaid, A. A. (1987). Mean residual life ordering. Statistical papers. To appear.

  • Barlow, R. E. and Proschan, F. (1975). Statistical Theory of Reliability and life testing. Holt, Rinehart & Winston, New York.

    MATH  Google Scholar 

  • Bhattacharjee, M. C. (1982). The class of mean residual lives and some consequences. SIAM. J. ALG. DISC. METH., 3, 56–65.

    Article  MATH  MathSciNet  Google Scholar 

  • Bryson, M. C. and Siddiqui (1969). Some criteria for ageing. J. Amer. Statist. Ass., Vol. 64, 1472–1483.

    Article  MathSciNet  Google Scholar 

  • Hollander, M. and Proschan, F. (1975). Tests for the mean residual life. Biometrika, 62, 3. 585–593.

    Article  MATH  MathSciNet  Google Scholar 

  • Karlin, S. (1957). Polya-type distributions, II. Ann. Math. Statist., 28, 281–308.

    Article  MATH  MathSciNet  Google Scholar 

  • Karlin, S. (1968). Total Positivity, vol 1. Stanford University Press, Stanford, CA.

    MATH  Google Scholar 

  • Karlin, S. and Rubin, H. (1956). The theory of decision procedures for distributions with monotone likelihood ratio. Ann. Math. Statist., 27, 272–299.

    Article  MATH  MathSciNet  Google Scholar 

  • Keilson and Sumita (1982). Uniform stochastic ordering and related inequalities. Canad. J. Statist.,

  • Kotz, S. and Shanbhag, D. N. (1980). Some new approaches to probability distributions. Adv. Appl. Prob. 12, 903–921.

    Article  MATH  MathSciNet  Google Scholar 

  • Lehmann, E. L. (1955). Ordered families of distributions. Ann. Math. Statist., 26, 399–419.

    Article  MATH  MathSciNet  Google Scholar 

  • Muth, E. J. (1980). Memory as a property of probability distributions. IEEE. Trans. Rel., R-29, 160–164.

    MATH  Google Scholar 

  • Pinedo, M. and Ross, M. S. (1980). Scheduling jobs subject to nonhomogeneous Poisson shocks. Management Science, 26, 1250–1257.

    MATH  MathSciNet  Google Scholar 

  • Ross, M. S. (1983). Stochastic Processes. Wiley, New York.

    MATH  Google Scholar 

  • Ross, M. S. and Schechner, Z. (1984). Some reliability application of the variability ordering. Oper. Res., 32, 679–687.

    Article  MATH  MathSciNet  Google Scholar 

  • Stoyan, D. (1983). Comparison Methods for Queues and other Stochastic Models. John Wiley, New York.

    MATH  Google Scholar 

  • Whitt, W. (1980). Uniform conditional stochastic order. J. Appl. Prob., 17, 112–123.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, College of Science, King Saud University, P.O. Box 2455, 11451, Riyadh, Saudi Arabia

    Abdul-Hadi N. Ahmed

Authors
  1. Abdul-Hadi N. Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ahmed, AH.N. Preservation properties for the mean residual life ordering. Statistical Papers 29, 143–150 (1988). https://doi.org/10.1007/BF02924519

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02924519

Keywords

Search

Navigation