Using the Discrete Lindley Distribution to Deal with Over-dispersion in Count Data

Count data in environmental epidemiology or ecology often display substantial over-dispersion, and failing to account for the over-dispersion could result in biased estimates and underestimated standard errors. This study develops a new generalized linear model family to model over-dispersed count data by assuming that the response variable follows the discrete Lindley distribution. The iterative weighted least square is developed to fit the model. Furthermore, asymptotic properties of estimators, the goodness of fit statistics are also derived. Lastly, some simulation studies and empirical data applications are carried out, and the generalized discrete Lindley linear model shows a better performance than the Poisson distribution model.