Bayesian inference for zero-inflated negative binomial lindley model of overdispersed count data with excess zeros

This article aims to develop the zero-inflated negative binomial-Lindley regression model to address the complexity of count data with zero excess and over-dispersion. The proposed compound distribution combines the zero generation mechanism with the Lindley distribution process, and the Bayesian hierarchical framework with MCMC sampling is adopted for parameter estimation, overcoming the limitations of traditional count models in handling complex data structures. The model is applied to two real datasets, one of which is characterized by a large number of zero observations. Its performance is compared with that of the NB-L and NB model. The results show that when the dataset presents the large number of zero values and the long tail feature, the ZINB-L GLM describes the dataset better than the other models.