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：通过将泊松变量与独立分布的迁移几何随机变量进行卷积，推导出一种新型过分散离散分布——PoiTG分布。该分布推广了几何分布、迁移几何分布及PoiG分布。系统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、生存函数及风险率函数。对模型随机序性质进行了详细分析。采用通用优化方法和EM算法获取参数的最大似然估计。研究表明，相较于现有最接近的竞争模型，所提分布有望为从业者处理过分散计数数据提供有效工具。