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.
