Modeling rare events using a zero-inflated poisson (ZIP) distribution: some new results on point estimator

This paper takes a fresh look on point estimation of model parameters under a Zero-Inflated Poisson (ZIP) distribution. The reason is that some finer details of point estimation, if overlooked, may lead to wrong estimates as was done by the earlier researchers. In this paper we have achieved the following new results: (a) A new set of corrected method of moments estimators has been proposed; (b) We have shown how the standard technique of differentiating the log-likelihood function to find the maximum likelihood estimators may lead to wrong estimates, as well as how to avoid this problem; and (c) A new adjusted maximum likelihood estimation technique has been proposed which not only produces meaningful estimates always, but also appears to work better compared to all other estimation techniques in terms of standardized mean squared error (SMSE) when ZIP is used to model rare events. Finally, datasets on rare events have been used to demonstrate the estimation techniques, and how the ZIP distribution can be used to model such datasets.