The Truncated Poisson Distribution

has been considered by David and Johnson in a recent issue of this journal [1]. In particular, they derive the maximum likelihood estimate of X and its asymptotic variance, and discuss the efficiency of estimation by moments. Distribution (ii) has been studied by Mloore [2], who provides a simple estimate of X and shows the effect of truncation at different values s. The purpose of the present note is to provide a similar estimate of X for distribution (i), to show that it is highly efficient, and to estimate its sampling variance. 2. Suppose that a sample of size N from a truncated Poisson distribution of type (i) gives N, observations equal to r(r = 1, 2, 3,) To estimate an arbitrary function 6(X), use quantities of the form