A novel model for count data: zero-inflated Probit Bell model with applications

A novel model for count data is proposed in this work. This new model is briefly called the Zero-Inflated Probit Bell (ZIPBell) model. The ZIPBell model can be used to simulate and analyze traditional count data and can be used well in the simulation and analysis of count data with the phenomenon that the frequency for zero occupies a very high percentage. In the scope of this study, we first provide the general formula, functions or related equations for the ZIPBell model. The results of asymptotic inferences for the ZIPBell model are also given in this work. Maximum likelihood estimator (MLE) is used to check its performance of the proposed model. According to the numerical illustrations via several simulation researches and the analysis of a practical data set, it has been seen that the MLE method has offered correct and reliable inferences. Finally, the inferences and conclusions of this study are mentioned.