A new approach on the renewal process with Geometric interarrival times
Journal Title: International Research Journal of Applied and Basic Sciences - Year 2013, Vol 4, Issue 6
Abstract
This paper develops the probability of a renewal process, whose interarrival are independent and identically distributed (i.i.d.) random variables (R.V.s) with geometric distribution. The distribution of the number of renewals in (0,t] and the joint distribution of the number of renewals in (0,a] and [a,b], 0 < a < b, are obtained. Then, using the joint distribution, the distribution of the number of renewals in [a,b], 0 < a < b, is obtained. Finally, we show that every renewal processes, whose interarrivals are i.i.d. discrete R.V.s, has independent and stationary increment if and only if its interarrivals be geometric distribution.
Authors and Affiliations
H. Samimi| Department of Statistics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran. samimi@guilan.ac.ir, Mohammad Mohammadi| Department of Statistics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.
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