Estimation in zero-inflated Generalized Poisson distribution

Kirtee K. Kamalja ； Yogita S. Wagh

《Journal of Data Science》 16卷1期 (2018/01) Pp. 183-206

https://doi.org/10.6339/JDS.201801_16(1).0010

摘要

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.

關鍵字

Zero-inflated Generalized Poisson ； Zero-inflated Negative Binomial ； simulation