Skip to main content
SpringerLink
Log in

A characterization of exponential distributions based on order statistics

  • Publications
  • Published:
Metrika Aims and scope Submit manuscript

Abstract

This note contains a characterization of exponential distributions based on the properties of linear transformations of order statistics. This is a certain converse of a well known theorem of Rényi about the distribution of linear combinations of order statistics from exponential distributions. Some statistical applications of the result are indicated.

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

  • Aczel, J.: Lectures on functional equations and their applications. New York 1966.

  • Ahsanullah, M.: On a characterization of the exponential distribution by order statistics. J. Appl. Prob.13, 1976, 818–822.

    Article  MathSciNet  MATH  Google Scholar 

  • Galambos, J.: Characterization of certain probability distributions by independence of order statistics. J. Appl. Prob.9, 1972, 224–230.

    Article  MATH  Google Scholar 

  • Govindarajulu, Z.: Characterization of exponential and power distributions. Skand. Aktuarietidskr. 49, 1966, 132–136.

    MathSciNet  MATH  Google Scholar 

  • Kagan, A.M., Yu. V. Linnik, andC.R. Rao: Characterization problems in mathematical statistics. New York 1973.

  • Lukacs, E.: Characteristic Functions. 2nd. ed. New York 1970.

  • Parzen, E.: Stochastic Processes. San Francisco 1962.

  • Rao, C.R.: Linear Statistical Inference and its applications. 2nd ed. New York 1972.

  • Rényi, A.: On the theory of order statistics, Acta Math. Acad. Sci. Hung.4, 1953, 191–232.

    Article  MathSciNet  MATH  Google Scholar 

  • Rossberg, H.J.: Characterizations of distribution functions by the independence of certain functions of order statistics. Sankhyā, A34, 1972, 111–120.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Washington, Seattle, USA

    C. B. Bell

  2. Indian Statistical Institute, Calcutta, India

    Y. Rama Krishna Sarma

Authors
  1. C. B. Bell
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. Rama Krishna Sarma
    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

Bell, C.B., Rama Krishna Sarma, Y. A characterization of exponential distributions based on order statistics. Metrika 27, 263–269 (1980). https://doi.org/10.1007/BF01893604

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01893604

Keywords

Search

Navigation