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：本文通过泊松变量与独立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。该分布同时推广了泊松分布和几何分布，可用于建模过度离散以及等离散计数数据。详细研究了该计数模型的多项重要统计性质，包括概率生成函数、矩生成函数、各阶矩、生存函数和风险函数。深入探讨了其单调性质，如对数凹性和随机序性质。提出了该模型参数的矩估计法和极大似然估计法。研究表明，与最接近的竞争模型相比，所提出的分布可能为实践者建模过度离散计数数据提供有效工具。