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A novel over-dispersed discrete distribution, namely the PoiTG distributionis derived by the convolution of a Poisson variate and an independentlydistributed transmuted geometric random variable. This distribution generalizesthe geometric, transmuted geometric, and PoiG distributions. Various importantstatistical properties of this count model, such as the probability generatingfunction, the moment generating function, the moments, the survival function,and the hazard rate function are investigated. Stochastic ordering for theproposed model are also studied in details. The maximum likelihood estimatorsof the parameters are obtained using general optimization approach and the EMalgorithm approach. It is envisaged that the proposed distribution may prove tobe useful for the practitioners for modelling over-dispersed count datacompared to its closest competitors.

A new count model based on Poisson-Transmuted Geometric convolution