Zero-inflated probit Bernoulli model: a new model for binary data

Abstract

This study proposes a new model in the family zero-inflated (ZI) binary models, it is called as a ZI Probit Bernoulli (ZIPBer) model. This model can be performed to model or simulate binary data that has an excessive amount of zero counts. At the framework of this research, we first introduce the classical formula, estimating equation (EE) and related functions for the ZIPBer model. Next, the results of asymptotic inferences for the ZIPBer model is studied based on the widespread regularity conditions. For the numerical illustrations, many simulation studies and a practical data set are executed in this paper. Specifically, we perform the fishing data set (FDS) to check the working effectiveness and robustness of the maximum likelihood estimation (MLE) approach in estimating parameters for the ZIPBer model. We also illustrate that this actual data set is more suitable for the proposed model: ZIPBer than other binary models such as logit, probit and ZIBer. The achieved results in this study are very unanimous with reality. It also illustrates that this is a dependable verification for us to know the solution as well as how to proceed to how to catch or take the most fish. This is the contribution of this work in terms of application. Finally, some crucial discussions and conclusions are given in this paper.