Abstract
Consider a renewal proess on the nonnegative real line with distribution function F(x). Then the backward or forward recurrence times Ut and Vt are , in general, non–independent r.v.s. and are indenpendence iff F(.) is exponential. Several authors have studied the characterizations of the exponential distribution and hence of the Poisson process by certain properties of the distributions of Ut and Vt.
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