  A new two-parameter discrete distribution, namely the PoiG distribution is
derived by the convolution of a Poisson variate and an independently
distributed geometric random variable. This distribution generalizes both the
Poisson and geometric distributions and can be used for modelling
over-dispersed as well as equi-dispersed count data. A number of important
statistical properties of the proposed count model, such as the probability
generating function, the moment generating function, the moments, the survival
function and the hazard rate function. Monotonic properties are studied, such
as the log concavity and the stochastic ordering are also investigated in
detail. Method of moment and the maximum likelihood estimators of the
parameters of the proposed model are presented. 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.
