Minimum Variance Unbiased Estimators for Poisson Probabilities

This paper considers the problem of estimating Poisson probabilities or relative frequencies and some extensions of that problem. It is shown how minimum variance unbiased estimators based on a simple random sample of 72 observations on a Poisson process may be easily developed. Variances of the estimators and estimators for their variances are derived. Comparisons with maximum likelihood estimators and with distribution-free relative frequency estimators are made and illustrated with two examples.