Recurrence Relation for Minimum Variance Unbiased Estimation of Certain Left‐Truncated Poisson Distributions

J. C. Ahuja

Journal of the Royal Statistical Society Series C, 1972, vol. 21, issue 1, 81-86

Abstract: The minimum variance unbiased estimators, g(z, n) and G(z, n), for the parameter of the Poisson distributions truncated on the left at zero and one respectively, based on a sample size n and sample total z, are obtained using one of the results for the generalized power series distribution. These estimators, which depend on Stirling numbers of the second kind and their linear combinations, are difficult to calculate even for small values of n and z. Recurrence relations for g(z, n) and G(z, n) are provided independent of Stirling numbers of the second kind and useful for tabulation purposes. Behaviour of these two estimators as functions of n and z is also examined.

Date: 1972
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