A new mixed negative binomial regression model to analyze factors influencing the number of patients with respiratory disease and long-term effects of lung cancer

Abstract

This article aims to develop a new mixed distribution which mixes the negative binomial (NB) distribution and the modified quasi-Lindley (MQL) distribution. The new mixed NB distribution is called the negative binomial-modified quasi Lindley (NB-MQL) distribution. Parameters of the distribution and its regression coefficient are estimated using a Bayesian approach. The NB-MQL linear regression model is applied with an actual dataset with the characteristics of overdispersion of the count response variable. The results show that the NB-MQL model describes the factors influencing the number of patients with respiratory disease and long-term effects of lung cancer better than the NB and Poisson regression models.