Asymmetric Probability Mass Function for Count Data Based on the Binomial Technique: Synthesis and Analysis with Inference

In this article, a new probability mass function for count data is proposed based on the binomial technique. After introducing the methodology of the newly model, some of its distributional characteristics are discussed in-detail. It is found that the newly model has explicit mathematical expressions for its statistical and reliability properties, which is not the case with many well-known discrete models. Moreover, it can be used as an effectively probability tool for modeling asymmetric over-dispersed data with leptokurtic shapes. The parameters estimation through the classical point of view have been done via utilizing the technique of maximum likelihood and Bayesian approaches. A MCMC simulation study is carried out to examine the performance of the estimators. Finally, two distinct real data sets are analyzed to prove the flexibility and notability of the newly model.