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A transformed geometric distribution in stochastic modelling
Institution:Department of Statistics and Insurance Science University of Piraeus, 80 Karaoli-Dimitriou Street 18534 Piraeus, Greece;Department of Mathematics, University of Ioannina 45110 Ioannina, Greece;Department of Mathematics, University of Bradford Bradford, West Yorkshire, BD7 1Dp, U.K.
Abstract:The analytical concepts of infinite divisibility and (0) unimodality are fundamental to the study of probability distributions in general and to discrete distributions in particular. In this paper, a one-one correspondence is established between these two important properties which will permit any infinitely divisible discrete distribution (with finite mean value) to be transformed into a (0) unimodal discrete distribution. When this transformation is applied specifically to the geometric distribution, the result is a novel distribution, which can be fully and explicitly specified and whose factorial moments can be expressed in closed forms. This transformed geometric distribution is found to apply to underreported geometrically distributed decision processes, embedded renewal processes with logarithmically distributed components, and M/M/1 queues in which the service mechanism has been uniformly improved.
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