A Novel Two-Parameter Contiguous Zero-inflated Model for Count Data

Abstract

This paper proposes a novel two-parameter contiguous zero-inflated distribution derived from the joint distribution of the three-parameter gamma and Poisson distributions, based on Lakshmi's three-parameter gamma distribution. The distribution’s properties and common descriptive statistical measures were derived. The study explores the probability mass function, coefficient of variation, skewedness, and kurtosis in relation to parameter changes and discusses parameter estimation using maximum likelihood and moment-generating function methods. Simulation studies evaluate the consistency and efficiency of the distribution at varying sample sizes and parameters. The model's application to the number of deaths demonstrates its flexibility in capturing excess zeros and over-dispersion in count data, providing a better alternative to some existing zero-inflated models.