On a “lack of memory” property

  • J. S. Huang


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.

AMS 1970 subject classifications

60E05 60H20 62E10 

Key words

Exponential distribution characterization lack of memory nonlattice distribution Laplace transform analytic continuation Wiener-Hopf technique 


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Copyright information

© The Institute of Statistical Mathematics, Tokyo 1981

Authors and Affiliations

  • J. S. Huang
    • 1
  1. 1.University of GuelphGuelphCanada

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