Biased-Reduced Maximum Likelihood Estimation for the Zero-Inflated Poisson Distribution

We investigate the small-sample quality of the maximum likelihood estimators (MLEs) of the parameters of the zero-inflated Poisson distribution. The finite-sample biases are determined to O(n) using an analytic bias reduction methodology based on the work of Cox and Snell (1968) and Cordeiro and Klein (1994). Monte Carlo simulations show that the MLEs have very small percentage biases for this distribution, but the analytic bias reduction methods essentially eliminate the bias without adversely affecting the mean squared error s of the estimators. The analytic adjustment compares favourably with the parametric bootstrap bias-corrected estimator, in terms of bias reduction itself, as well as with respect to mean squared error and Pitman’s nearness measure.