Estimating the Ratio of Means in a Zero-Inflated Poisson Mixture Model

The problem of estimating the ratio of the means of a two-component Poisson mixture model is considered, when each component is subject to zero-inflation, i.e., excess zero counts. The resulting zero-inflated Poisson mixture (ZIPM) model can be viewed as a three-component Poisson mixture model with one degenerate component. The EM algorithm is applied to obtain frequentist estimators and their standard errors, the latter determined via an explicit expression for the observed information matrix. As an intermediate step, we derive an explicit expression for standard errors in the two-component Poisson mixture model (without zero-inflation), a new result. The ZIPM model is applied to simulated data and real ecological count data of frigatebirds on the Coral Sea Islands off the coast of Northeast Australia.