Abstract
Overdispersion is a common phenomenon in Poisson modelling. The generalized Poisson (GP) distribution accommodates both overdispersion and under dispersion in count data. In this paper, we briefly overview different overdispersed and zero-inflated regression models. To study the impact of fitting inaccurate model to data simulated from some other model, we simulate data from ZIGP distribution and fit Poisson, Generalized Poisson (GP), Zero-inflated Poisson (ZIP), Zero-inflated Generalized Poisson (ZIGP) and Zero-inflated Negative Binomial (ZINB) model. We compare the performance of the estimates of Poisson, GP, ZIP, ZIGP and ZINB through mean square error, bias and standard error when the samples are generated from ZIGP distribution. We propose estimators of parameters of ZIGP distribution based on the first two sample moments and proportion of zeros referred to as MOZE estimator and compare its performance with maximum likelihood estimate (MLE) through a simulation study. It is observed that MOZE are almost equal or even more efficient than that of MLE of the parameters of ZIGP distribution.
Highlights
Statistical models that address the count data have been implemented in many areas such as insurance, dental epidemiology, health care facilities, risk classification, medicine, etc
We present the results of a simulation study, which fits Poisson (P), generalized Poisson (GP), Zero-inflated Poisson (ZIP), Zero-inflated Generalized Poisson (ZIGP) and Zero-inflated Negative Binomial (ZINB) model to the sample data from ZIGP distribution
The simulation study in this paper demonstrates that the new estimators θ θ3, φ φ3 of θθ and φφ are almost efficient as that of respective maximum likelihood estimate (MLE) while ω ω3 is much more efficient than ω ωMMMMMM
Summary
Statistical models that address the count data have been implemented in many areas such as insurance, dental epidemiology, health care facilities, risk classification, medicine, etc. The Poisson model is a standard approach to analyze the count data. The most annoying property of Poisson model is equality of mean and variance, which is known as equidispersion. The sample data often has variance which exceeds its mean. The phenomenon of excess variability is called overdispersion and has been widely studied in the literature (Dean and Lawless (1989) and Dean (1992). Failure to properly address existing overdispersion leads to serious underestimation of standard errors and misleading inference for the regression
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