Poisson-Modification of Quasi Lindley regression model for over-dispersed count responses

Abstract

This paper introduces an alternative linear regression model for over-dispersed count responses with appropriate covariates. It is an extended work of univariate Poisson-Modification of the Quasi Lindley (PMQL) distribution via the generalized linear model approach. A re-parametrized PMQL distribution is considered to demonstrate the flexible properties of the distribution on its regression model. Further, the performance of its maximum likelihood estimation method is examined by a simulation study based on the asymptotic theory. The maximum likelihood estimator is used to estimate the parameters of the regression model. Finally, three simulated data sets and a real-world data set are taken to show the applicability of the PMQL regression model against the Poisson, Negative binomial (NB), Poisson-Quasi Lindley (PQL), and Generalized Poisson-Lindley (GPL) regression models. The results of applications show that the newly introduced model provides a better fit for over-dispersed count responses with covariates than the Poisson, NB, PQL, GPL regression models.