Bayesian Inference for Negative Binomial-Beta Exponential Distribution and Its Regression Model

This article provided the particular properties of the negative binomial-beta exponential (NB-BE) distribution and extended to its regression model. The model parameters were estimated using the Bayesian inference method. We utilize the NB-BE distribution and NB-BE regression model to apply with real data. In addition, the model performance was compared with some traditional models. For developing the NB-BE regression model, it was performed under a generalized linear model framework and slightly adjusted the parameterization. The research results showed that the NB-BE distribution is more appropriate than the Poisson and negative binomial distributions. Accordingly, the NB-BE regression model can be applied to analyze such over-dispersed datasets. For model selection, three criteria are considered which are the deviance, the effective number of parameters, and deviance information criterion. It is found that the proposed regression model shows the smallest values of deviance, the effective number of parameters, and the deviance information criterion. Consequently, this regression model relevant to the NB-BE distribution outperforms both the Poisson and the negative binomial regression models. Therefore, it is an alternative and useful regression model for the utilization of two real data applications with over-dispersion.