On a “lack of memory” property
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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 classifications60E05 60H20 62E10
Key wordsExponential distribution characterization lack of memory nonlattice distribution Laplace transform analytic continuation Wiener-Hopf technique
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