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.

翻译：通过泊松变量与独立分布几何随机变量的卷积，推导出一种新的双参数离散分布，即PoiG分布。该分布推广了泊松分布和几何分布，可用于建模过离散及等离散计数数据。本文研究了所提出计数模型的若干重要统计性质，包括概率母函数、矩母函数、各阶矩、生存函数和风险率函数。同时详细探讨了其单调性质，如对数凹性及随机序关系。给出了所提模型的矩估计方法和参数的最大似然估计量。预期与最接近的竞争模型相比，所提出的分布能为实际工作者处理过离散计数数据提供更有效的建模工具。