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:PoiG分布是由Poisson变量和独立分布的几何随机变量的组合产生的,这种分布概括了Poisson和几何分布,可用于模拟超分散和等分散的计数数据。拟议计数模型的一些重要统计属性,如概率生成功能、时刻生成功能、时刻、存续功能和危险率函数。研究了单调特性,如对日志凝固和随机顺序也进行了详细调查。提出了时间方法和拟议模型参数的最大概率估测器,设想拟议的分布可能证明有助于从业者与最接近的竞争者相比,模拟超分散计数数据。