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 {\it zero-inflated Poisson mixture (ZIPM) model} can be treated 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. Bayes and empirical Bayes estimators also are obtained by means of conjugate priors and their data-based variants. Lastly, the ZIPM distribution and the ZTP (zero-truncated Poisson) distribution are compared.