On the Univariate and Multivariate Applications of the Poisson Two Parameter Chris-Jerry Distribution to Count Data

Abstract

Statistical analysis and data modeling are necessary in explaining and extracting important information from real-world scenarios. In this study, we illustrated the univariate and multivariate applications of the Poisson two parameter Chris-Jerry (PTPCJ) distribution proposed by [9]. The features of the PTPCJ distribution indicate that the distribution is flexible for modeling positively skewed and approximately symmetric datasets. The PTPCJ distribution has a dispersion index greater than one. That makes it suitable for modeling count data which exhibit over-dispersed characteristic. Thus, we illustrated the univariate applicability of the PTPCJ distribution utilizing three datasets, and in all cases, it outperforms the competing models. Furthermore, multivariate application is demonstrated using  the PTPCJ regression model when the response variable conforms to the PTPCJ distribution. The applicability of the regression model shows its superiority in modeling count data.