Abstract
The estimation of restricted parameters by fixed sample size rules has been considered by Hammersley [1]. A sequential solution to the problem of estimating the mean of a normal distribution when it is some unknown integer and a general method for solving problems of this sort were studied by Robbins in [4]. Based on the work of Robbins, a sequential procedure for estimating the parameter of a Poisson distribution when it is known to be an integer was given in [3]. The results obtained herein represent a generalization of the work dealing with the normal and Poisson cases. A class of sequential procedures is proposed and bounds on the error probabilities are obtained. The expected sample sizes are investigated and a weak form of optimality is demonstrated under certain conditions.
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