On Interval Estimation of the Poisson Parameter in a Zero-inflated Poisson Distribution

Abstract

The zero-inflated Poisson distribution is the most widely applied model for count data with excessive zeros. In this paper, confidence intervals for the Poisson parameter are derived by using score statistics. The resulting intervals are compared to the Wald confidence interval (WCI), which stems from properties of the asymptotic normal distribution. For interval constructions, a Bernoulli parameter, known as a nuisance parameter, is eliminated by the profile likelihood approach. The Wald-type intervals can be formulated explicitly, while the score intervals have no closed forms. Furthermore, the observed and expected Fisher information matrices are shown to be the same. Using a simulation study, the confidence intervals are compared in many situations where the Poisson and Bernoulli parameters and sample sizes are varied. The coverage probability (CP), average length, and coverage per unit length (CPUL) are obtained from Monte Carlo methods. The results reveal that the score confidence intervals are superior to the WCIs in an aspect of CP with small sample sizes, but all of these intervals are comparable in terms of CPUL.