ON INTERVAL ESTIMATION OF THE POISSON PARAMETER IN A ZERO-TRUNCATED POISSON DISTRIBUTION

Abstract

When the research outcome is counts of a rare event, Poisson distribution is a first choice to describe the population distribution under study. However in some applications, the zero count would not be observed at all. In such cases the model to be fitted to the data is a zero-truncated Poisson (ZTP) distribution. This distribution is a special case of the more general zero-modified Poisson (ZMP) distribution family. This article discusses estimation procedures for the Poisson parameter of the ZTP model. In particular, performance of confidence intervals in terms of coverage probability is fully examined by Monte Carlo simulations. It is shown that the score-type interval behaves well but the Wald-type interval gives unsatisfactory results if the Poisson mean is small and/or sample size is not so large. A modification of the Wald-type interval is also given, and its performance is investigated by using simulations. The findings are also applicable to ZMP distributions.