Bayesian inference for the negative binomial-generalized Lindley regression model: properties and applications

This article aims to develop a new linear model for count data, which is called the negative binomial - generalized Lindley (NB-GL) regression model. The NB-GL distribution has been proposed and applied to count data analysis, which is constructed as a mixture of the negative binomial and generalized Lindley distributions. The NB-GL distribution has the special sub-models, such as the negative binomial - Lindley, negative binomial - gamma, and negative binomial - exponential distributions. Parameters of the distribution and its regression model are estimated using a Bayesian approach. The NB-GL regression model is applied to fit real data sets. Its performance is compared with some traditional models. The results show that the generalized linear model for the NB-GL model describes the data sets better than other models.