A generalization to zero-inflated hyper-Poisson distribution: Properties and applications

Abstract

The zero-inflated models have becomes fairly popular in the research literature. Medical and public health research involve the analysis of count data that exhibits a substantially large proportion of zeroes. The first zero-inflated model is the zero-inflated Poisson model, which concerns a random event containing excess zero-count in unit time. In this paper we consider a zero-inflated version of the modified hyper-Poisson distribution as a generalization of the zero-inflated Hyper-Poisson distribution of Kumar and Ramachandran (Commun.Statist.Simul.Comp., 2019) and study some of its important properties through deriving its probability generating function and expressions for factorial moments, mean, variance, recursion formulae for factorial moments, raw moments and probabilities. The estimation of the parameters of the proposed distribution is attempted and it has been fitted to certain real life data sets to test its goodness of fit. Further, certain test procedures are constructed for examining the significance of the parameters of the model and a simulation study is carried out for assessing the performance of the maximum likelihood estimators of the parameters of the distribution.

Keywords:

• Confluent hypergeometric function
• Count data modeling
• Model selection
• Rao’s efficient score test
• Simulation
• Zero-inflated distribution

Acknowledgments

The authors are highly thankful to the Editor in Chief, the Associate Editor and the anonymous referees for their fruitful comments, which immensely helped to improve the quality and presentation of the paper.

Additional information

Funding

The first author is particularly thankful to Department of Science and Technology, New Delhi (Government of India) for financial support (MTR/2017/000942).