Poisson copoun distribution: An alternative discrete model for count data analysis

In this article, we have propounded a novel two-parameter count probability model by compounding the Poisson distribution with the Copoun distribution. This model is versatile in terms of its probability mass and hazard rate functions. To evaluate the constructiveness of the proposed model, various statistical properties, including moments, moment-generating function, probability-generating function, factorial moments, Rényi entropy, Shannon entropy, and order statistics, have been derived efficaciously. The parameters of the new model are estimated by using the maximum likelihood estimation technique. The behavior of the derived estimates is examined by conducting comprehensive simulation study. The flexibility and effectiveness of the proposed distribution were evaluated by applying it to three real-life datasets from different fields. The results indicate that the new distribution analyzed these datasets more efficiently than competing distributions. As a flexible extension of the Poisson distribution, this model is particularly suitable for analyzing over-dispersed count data.