  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.
