On a lack of memory property of the exponential distribution

  • R. Shimizu


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.


Exponential Distribution Periodic Function Moment Generate Function Irrational Number Memory Property 


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  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

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© The Institute of Statistical Mathematics, Tokyo 1979

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  • R. Shimizu

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