Single and Double Ratio Estimators for the Poisson Parameter

Classical parameter estimation for Poisson-distributed data relies mainly on maximum likelihood estimation (MLE), which assumes that the data perfectly adhere to the model assumptions, including equidispersion. However, real-world datasets often suffer from structural discrepancies that violate these assumptions, leading to biased estimates and inflated mean squared errors. This study derives two estimators—simple ratio (SR) and double ratio (DR) estimators—which are based on ratios of observed frequencies around the mode of the data. Consistency of the estimators is established analytically. Using a Monte Carlo simulation, we evaluate the performance of these estimators across four critical scenarios: outliers, right truncation, zero-inflation, and zero-truncation. In all these scenarios, the proposed estimators showed consistent behavior and, in most scenarios, superior performance to the MLE, especially for larger sample sizes. Real data examples illustrate the proposed estimators.