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

TL;DR

This paper develops methods to estimate the ratio of means in a zero-inflated Poisson mixture model, using EM algorithms, Bayesian approaches, and distribution comparisons, addressing excess zeros in count data.

Contribution

It introduces a comprehensive framework for estimating mean ratios in ZIPM models, including EM, Bayesian, and empirical Bayesian estimators, with explicit variance calculations.

Findings

EM algorithm provides consistent estimators with standard errors.

Bayesian and empirical Bayes estimators are derived using conjugate priors.

Comparison shows differences between ZIPM and ZTP distributions.

Abstract

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.