Advertisement

On a lack of memory property of the exponential distribution

  • R. Shimizu
Article

Summary

LetX be a positive random variable with the distributionF and letG0 be a monotone non-decreasing function such that E{G0(X)} exists and is positive. Then under some additional conditions onF andG0, E{G0(X−x)|X>x}=E{G0(X)},x≧0 implies thatF is exponential.

Keywords

Exponential Distribution Periodic Function Moment Generate Function Irrational Number Memory Property 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Azlarov, T. A., Dzamirzaev, A. A. and Sultanova, M. M. (1972). These papers were not available to the author at the time of writing this paper (c.f. Galambos-Kotz [3]). Characterization properties of the exponential distribution and their stability,Sluchain. Proc. i Statist. Vyvody,2, Tashkent, Fan, 10–19 (in Russian).Google Scholar
  2. [2]
    Dallas, A. C. (1975). These papers were not available to the author at the time of writing this paper (c.f. Galambos-Kotz [3]). On a characterization by conditional variance,Manuscript, Athens University, Greece.Google Scholar
  3. [3]
    Galambos, J. and Kotz, S. (1978).Characterizations of Probability Distributions, Lecture Notes in Mathematics 675, Springer-Verlag.Google Scholar
  4. [4]
    Huang, J. S. (1978). On a “lack of memory” property,University of Guelph Statistical Series, 1978–84.Google Scholar
  5. [5]
    Klebanov, L. B. (1977). Some results related to characterization of the exponential distributions, Pre-print in Russian, to appear inTheory Prob. its Appl. Google Scholar
  6. [6]
    Laurent, A. G. (1974). On characterization of some distributions by truncation properties,Amer. Statist. Ass.,69, 823–827.MathSciNetCrossRefGoogle Scholar
  7. [7]
    Marsaglia, G. and Tubilla, A. (1975). A note on the “lack of memory” property of the exponential distribution,Ann. Prob.,3, 353–354.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Ramachandran, B. (1977). On the strong Markov property of the exponential laws,Proceedings of the Colloquium on the Methods of Complex Analysis in the Theory of Probability and Statistics, Debrecen, Hungary, Aug–Sept., 1977.Google Scholar
  9. [9]
    Ramachandran, B. (1979). On the “Strong Memoryless property” of the exponential and geometric probability laws, Pre-print, Indian Statist. Institute, New Delhi, India.zbMATHGoogle Scholar
  10. [10]
    Sahobov, O. M. and Geshev, A. A. (1974). These papers were not available to the author at the time of writing this paper (c.f. Galambos-Kotz [3]). Characteristic properties of the exponential distribution,Natura Univ. Plovidiv.,7, 25–28 (in Russian).Google Scholar
  11. [11]
    Shimizu, R. (1978). Solution to a functional equation and its application to some characterization problems,Sankyã, A,40, in press.Google Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1979

Authors and Affiliations

  • R. Shimizu

There are no affiliations available

Personalised recommendations