A new two-parameter over-dispersed discrete distribution with mathematical properties, estimation, regression model and applications

This paper focuses on the derivation of a new two-parameter discrete probability distribution. The new model is derived by mixing Poisson and Loai distributions and is named "Poisson Loai Distribution". The paper explores various mathematical properties of the new model, introducing a count-regression model based on this distribution. The parameters of the model are estimated using the maximum likelihood estimation method. A comprehensive simulation study is utilized to assess the behavior of derived estimators. The importance of the proposed distribution is confirmed through the analysis of three real datasets. It is found that the suggested distribution has the greatest match when compared to all rival distributions, and it may be a viable alternative for assessing dispersed count data.