An integrated lack of memory characterization of the exponential distribution

  • E. Grosswald
  • Samuel Kotz


In this note a charactrization of the exponential distribution is discussed based on yet another extension of the lack of memory property. The result was motivated by a functional equation appearing in Ahsannulah [1], [3]

Key word

Exponential distribution geometric distribution characterization lack of memory replacement procedures hazard rate Fourier-Laplace transform 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Ahanullah, M. (1976). On a characterization of the exponential distribution by order statistics,J. Appl. Prob.,13, 818–822.CrossRefGoogle Scholar
  2. [2]
    Ahsanullah, M. (1977). A characteristic property of the exponential distribution,Ann. Statist.,5, 580–582.MathSciNetMATHGoogle Scholar
  3. [3]
    Ahsanullah, M. (1978). A characterization of the exponential distribution by spacings,J. Appl. Prob.,15, 650–653.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    Doetsch, G. (1950).Handbuch der Laplace Transformation, 3 Vol., Verlag Birkhäuser, Basel.MATHGoogle Scholar
  5. [5]
    Gaver, D. P. and Acar, M. (1979). Analytical hazard representations for use in relability, mortality and simulation studies.Commun. Statis.—Simula. Computa., B8 (2), 91–111.MathSciNetGoogle Scholar
  6. [6]
    Grosswald, E., Kotz, S. and Johnson, N. L. (1979). Characterization of the exponential distribution by relevation type equations,Intitute of Statistics Mimeo Series#1218, University of North Caroline, Chapel Hill,J. Appl. Prob.,17, 874–877.MathSciNetCrossRefGoogle Scholar
  7. [7]
    Johnson, N. L. and Kotz, S. (1970).Continuous Univariate Distributions, Vol. 1, Wiley, New York.MATHGoogle Scholar
  8. [8]
    Krakowski, M. (1973). The relevation transform and a generalization of the gamma distribution function,Rev. Française Auf. Inf. Rech. Opérat.,7, Sér. V-2. 107–120.MathSciNetGoogle Scholar
  9. [9]
    Shimizu, R. (1978). Solution to a functional equation and its application to some characterization problems,Research Memorandum No. 131, The Institute of Statistical Mathematics, Tokyo (to appear inSankyã, Ser. A).Google Scholar
  10. [10]
    Shanbhag, D. N. (1977). An extension of the Rao-Rubin characterization of the Poisson distribution,J. Appl. Prob.,14, 640–646.MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    Titchmarsh, E. C. (1939).The Theory of Functions, (2nd ed.), The Clarendon Press Oxford, England.MATHGoogle Scholar
  12. [12]
    Titchmarsh, E. C. (1948).Introduction to the Theory of Fourier Integrals, (2nd ed.), The Clarendon Pres Oxford, England.Google Scholar
  13. [13]
    Zygmund, A. (1955).Trigonometrical Series, Dover Publications.Google Scholar

Copyright information

© Kluwer Academic Publishers 1981

Authors and Affiliations

  • E. Grosswald
    • 1
    • 2
  • Samuel Kotz
    • 1
    • 2
  1. 1.Temple UniversityTampleUSA
  2. 2.University of MarylandUSA

Personalised recommendations