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.

翻译：本文通过泊松变量与独立分布的变换几何随机变量的卷积，推导出一种新的过离散离散分布，即PoiTG分布。该分布推广了几何分布、变换几何分布和PoiG分布。研究了该计数模型的各种重要统计性质，如概率生成函数、矩生成函数、矩、生存函数和风险率函数。同时详细探讨了所提模型的随机序问题。采用通用优化方法和EM算法方法获得了参数的最大似然估计量。预计与最接近的竞争模型相比，所提出的分布可为实践者处理过离散计数数据建模提供更有效的工具。