2023/01/04 by Anupama Nandi, Subrata Chakraborty, Nandi, Anupama +3
Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2301.01480
openalex publication_date 2023/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.