Binomial Poisson Ailamujia model with statistical properties and application

In this study, an improved extension of the Poisson-Ailamujia distribution is introduced. The new distribution was derived using a binomial mixing approach, and the new model is named the “Binomial Poisson-Ailamujia (Bin-PA)” distribution. Some important statistical properties are derived, including mode, quantile function, moments and their associated measures, actuarial (risk) measures, and reliability features such as survival, hazard (failure) rate, and mean residual life function. The parameters of the proposed distribution are estimated using the maximum likelihood estimation method. A comprehensive simulation study is also carried out to access the behavior-derived maximum likelihood estimators. Furthermore, a new count-regression model was also introduced. Two datasets are utilized to demonstrate the applicability and usefulness of the new model. It is concluded that the Binomial Poisson-Ailamujia distribution is more flexible and efficiently analyzed both datasets as compared to competitive discrete distributions.