  A novel over-dispersed discrete distribution, namely the PoiTG distribution
is derived by the convolution of a Poisson variate and an independently
distributed transmuted geometric random variable. This distribution generalizes
the geometric, transmuted geometric, and PoiG distributions. Various important
statistical properties of this count model, such as the probability generating
function, the moment generating function, the moments, the survival function,
and the hazard rate function are investigated. Stochastic ordering for the
proposed model are also studied in details. The maximum likelihood estimators
of the parameters are obtained using general optimization approach and the EM
algorithm approach. It is envisaged that the proposed distribution may prove to
be useful for the practitioners for modelling over-dispersed count data
compared to its closest competitors.
