Skip to main content
SpringerLink
Log in

On a characterization of the exponential distribution by spacings

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Summary

LetX be a non-negative random variable with probability distribution functionF. SupposeX i,n (i=1,…,n) is theith smallest order statistics in a random sample of sizen fromF. A necessary and sufficient condition forF to be exponential is given which involves the identical distribution of the random variables (n−i)(X i+1,n−Xi,n) and (n−j)(X j+1,n−Xj,n) for somei, j andn, (1≦i<j<n).

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

  1. Aczél, J. (1966).Lectures on Functional Equations and Their Applications, Academic Press, New York.

    MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  3. Ahsanullah, M. (1977). A characteristic property of the exponential distribution,Ann. Statist.,5, 580–582.

    Article  MathSciNet  Google Scholar 

  4. Barlow, R. E. and Proschan, F. (1975).Statistical Theory of Reliability and Life Testing Probability Models, Holt, Rinehart and Winston Inc., New York.

    MATH  Google Scholar 

  5. Galambos, J. (1975). Characterization of probability distributions by properties of order statistics I,Statistical Distribution in Scientific Work,3, 71–88 (G. P. Patil et al., eds.), Reidel, Dordrecht.

    Chapter  Google Scholar 

  6. Govindarajulu, Z. (1966). Characterization of the exponential and power distributions,Skand. Aktuarietidskr.,10, 132–136.

    MathSciNet  MATH  Google Scholar 

  7. Kotz, S. (1974). Characterizations of statistical distribution, a supplement to recent survey,Rev. Int. Statist. Inst.,42, 39–65.

    Article  MathSciNet  Google Scholar 

  8. Puri, P. S. and Rubin, H. (1970). A characterization based on absolute difference of two i.i.d. random variables,Ann. Math. Statist.,41, 2113–2122.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Health Protection Branch, HWC, Ottawa

    M. Ahsanullah

Authors
  1. M. Ahsanullah
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The work was partly completed when the author was at the Dept. of Statistics, University of Brasilia, Brazil.

About this article

Cite this article

Ahsanullah, M. On a characterization of the exponential distribution by spacings. Ann Inst Stat Math 30, 163–166 (1978). https://doi.org/10.1007/BF02480209

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02480209

Key Words and Phrases

Search

Navigation