Modelling zero inflated and under-reported count data

Abstract

Poisson distribution is a classic choice for modelling unbounded count data. However, count data arising in various fields of scientific research often have excess zeros and are under-reported. In such situations, Poisson distribution gives a poor fit and Poisson model based inferences lead to biased estimators and inaccurate confidence intervals. In this paper we develop a flexible model which can accommodate excess zeros and undercount. Internal validation data has been used for making likelihood based inferences. The impact of ignoring undercount and excess zeros are studied through extensive simulations. The finite sample behaviour of the estimators are investigated through bootstrap methodology. Finally, a real life data which is supposedly under-reported and known to have excess zeros is analysed.

Keywords:

• Excess zero
• undercount
• surrogate
• likelihood
• bootstrap method

Mathematics Subject Classifications:

• 62F10
• 62F40
• 62P25
• 62P20

Acknowledgments

The authors thank the referees for careful reading of the manuscript and making constructive suggestions that resulted in a considerably improved present version.

Disclosure statement

No potential conflict of interest was reported by the author(s).