Skip to main content
SpringerLink
Log in

On a “lack of memory” property

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

Abstract

For two independent nonnegative random variablesX andY we say thatX is ageless relative toY if the conditional probability P[X> Y+x|X>Y] is defined and is equal to P[X>x] for allx>0. Suppose thatX is ageless relative to a nonlatticeY with P[Y=0]<P [Y<X]. We show that the only suchX is the exponential variable. As a corollary it follows that exponential variable is the only one which possesses the ageless property relative to a continuous variable.

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

    MATH  Google Scholar 

  2. Barlow, R. and Proschan, F. (1975).Statistical theory of reliability and life testing probability models, Holt, Rinehart and Winston, New York.

    MATH  Google Scholar 

  3. Cinlar, E. and Jagers, P. (1973). Two mean values which characterize the Poisson process,J. Appl. Prob.,10, 678–681.

    Article  MathSciNet  Google Scholar 

  4. Feller, W. (1967).An introduction to probability theory and its applications, 1, 3rd ed., Wiley, New York.

    MATH  Google Scholar 

  5. Krishnaji, N. (1970). Characterization of the Pareto distribution through a model of underreported incomes,Econometrica,38, 251–255.

    Article  Google Scholar 

  6. Krishnaji, N. (1971). Note on a characterizing property of the exponential distribution,Ann. Math. Statist.,42, 361–362.

    Article  Google Scholar 

  7. Marsaglia, G. and Tubilla, A. (1975). A note on the “lack of memory” property of the exponential distribution,Ann. Prob.,3, 353–354.

    Article  MathSciNet  Google Scholar 

  8. Obreteno, A. (1970). A property of the exponential distribution (Bulgarian),Fiz.-Mat. Spis. B″ lgar. Akad. Nauk.,13 (46), 51–53.

    Google Scholar 

  9. Ramachandran, B. (1977). On the strong Markov property of the exponential laws, paper contributed to theColloquium on the Methods of Complex Analysis in the Theory of Probability and Statistics, held at Debrecen, Hungary, Aug.-Sept.

  10. Rossberg, H.-J. (1972). Characterization of the exponential and the Pareto distributions by means of some properties of the distributions which the differences and quotients of order statistics are subject to,Math. Operat. u. Statist.,3, 207–216.

    Article  MathSciNet  Google Scholar 

  11. Shimizu, R. (1978). Solution to a functional equation and its application to some characterization problems,Sankhyā, A,40, 319–332.

    MathSciNet  MATH  Google Scholar 

  12. Widder, D. (1946).The Laplace transform, Princeton Univ. Press, Princeton.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Guelph, Guelph, Canada

    J. S. Huang

Authors
  1. J. S. Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research partially supported by NRC of Canada grants #A8057 and #T0500.

Work partially completed while on leave at Division of Math. Stat., C.S.I.R.O., Australia.

About this article

Cite this article

Huang, J.S. On a “lack of memory” property. Ann Inst Stat Math 33, 131–134 (1981). https://doi.org/10.1007/BF02480926

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02480926

AMS 1970 subject classifications

Key words

Search

Navigation