A Comparison of Properties of Three Estimators of the Parameters of a Poisson Distribution Truncated below One, When the Sample Size is Small.

摘要

This paper examines properties of three estimators of the parameter of a Poisson distribution truncated below one. For small sample sizes, namely, samples of 1, 2, and 5, it was shown that using the criterion of the expected squared error of estimate, the maximum likelihood estimator and the sample mean, both of which are biased, are admissible, while the best unbiased estimator is inadmissible. It becomes admissible only when its expected squared error coincides with that of the maximum likelihood estimator when n = 5. (Author)