An improved estimator of the mean for a sequential binomial sampling plan

For sampling Bernoulli random variables, a sequential sampling plan is considered that includes inverse sampling as a special case. This plan is viewed as a random walk in two dimensions in a way that gives the distribution of the sample given the endpoint of the walk. Thus, by the Rao-Blackwell method, an unbiased estimator based on the minimal sufiicient statistic is derived for the common Bernoulli probability. The techniques used apply in general to unbiased estimation when sampling sequentially, at least conceptually, and are also applied to a second class of sequential binomial sampling plans.