  In this work, we are interested in the stability and robustness of the
parameter estimation in the Zero-Inflated Bernoulli (ZIBer) model, when the
susceptible probability (SP) model is modeled by numerous different binary
models: logit, probit, cloglog and generalized extreme value (GEV). To address
this problem, we propose the maximum likelihood estimation (MLE) method to
check its performance when different SP models are considered. Based on
numerical evidences through simulation studies and the analysis of a real data
set, it can be seen that the MLE approach has provided accurate and reliable
inferences. In addition, it can also be seen that for the empirical analysis,
the probit-ZIBer model is probably more suitable for the fishing data set than
the other models considered in this study. Besides, the results obtained in the
experimental analysis are also very consistent, compatible and very meaningful
in practice. It will help us to understand the importance of increasing
production while fishing.
