A Note on Inverse Sampling Procedures for Selecting the Best Binomial Population

Abstract

Two inverse sampling procedures, one that uses the classical vector-at-a-time observation rule and another that uses the play-the-winner observation rule, are shown to select the best of $k$ binomial populations with the same probability, independent of the probabilities of success. This shows that the play-the-winner rule is better from the point of view that both the sample size and number of failures of each population are stochastically smaller using play-the-winner than vector-at-a-time.