In:
Journal of Applied Probability, Cambridge University Press (CUP), Vol. 30, No. 1 ( 1993-03), p. 121-130
Abstract:
Let γ t and δ t denote the residual life at t and current life at t , respectively, of a renewal process , with the sequence of interarrival times. We prove that, given a function G , under mild conditions, as long as holds for a single positive integer n , then is a Poisson process. On the other hand, for a delayed renewal process with the residual life at t , we find that for some fixed positive integer n , if is independent of t , then is an arbitrarily delayed Poisson process. We also give some corresponding results about characterizing the common distribution function F of the interarrival times to be geometric when F is discrete. Finally, we obtain some characterization results based on the total life or independence of γ t and δ t .
Type of Medium:
Online Resource
ISSN:
0021-9002
,
1475-6072
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1993
detail.hit.zdb_id:
1474599-9
detail.hit.zdb_id:
219147-7
SSG:
3,2
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