Abstract

The primary objective of statistical modelling is to develop a mathematical structure that can capture the average effect of a given set of explanatory variables on the endogenous variable called regression models. Such models are used to quantify the uncertainty and study the heterogeneity in the populations. Statistical models and methods for the analysis of count data received much attention during the last decades due to their application in diverse areas like epidemiology, biology, public health, and many others. In this paper a new regression model for count data, based on Discrete Weibull geometric (DWG) distribution is developed and various methods for estimation of the model parameters are illustrated. The excess number of observed zeros in a count data set results when many individuals fail to experience the event of interest. The over-dispersion in the count data can arise for the dataset with too many responses with zero counts, which the Poisson and Negative Binomial distribution cannot predict correctly. This can be overcome by using the zero-inflated models.. In this paper a modification of the DWG regression model called zero-inflated DWG (ZIDWG) regression is also introduced, to model the count data sets with excess zeros. We also discussed the EM algorithm for the numerical computation of the maximum-likelihood estimates and MCMC method for the numerical computation of the bayes estimates of the model parameters. The performance of the models are numerically evaluated using different simulated datasets. The usefulness of the newly developed models are illustrated using different real datasets and models were compared using the AIC and BIC values.