Zero-Modified Poisson-Lindley distribution with applications in zero-inflated and zero-deflated count data

TL;DR

This paper introduces the zero-modified Poisson-Lindley distribution, an extension of the zero-inflated Poisson-Lindley, for modeling zero-inflated and zero-deflated count data, with inference and real data applications.

Contribution

It proposes a new zero-modified Poisson-Lindley distribution with a parameter for zero-inflation or deflation, and compares estimation methods including bootstrap bias correction.

Findings

The new model fits real data better than existing models.

Maximum likelihood estimators are effective in small and large samples.

Bootstrap bias correction improves parameter estimation.

Abstract

The main object of this article is to present an extension of the zero-inflated Poisson-Lindley distribution, called of zero-modified Poisson-Lindley. The additional parameter $\pi$ of the zero-modified Poisson-Lindley has a natural interpretation in terms of either zero-deflated/inflated proportion. Inference is dealt with by using the likelihood approach. In particular the maximum likelihood estimators of the distribution's parameter are compared in small and large samples. We also consider an alternative bias-correction mechanism based on Efron's bootstrap resampling. The model is applied to real data sets and found to perform better than other competing models.