Sequential d-Posterior Multinomial Selection Procedure with Asymmetric Indifference Zone

A selection problem for finding the most probable outcome of a multinomial distribution is considered. We present a sequential procedure for solving a d-posterior variation of the problem. Here we suppose that one of the outcomes has a priority for us and should be selected if its probability is at least as great as any other. For the others to be selected, their probabilities should be greater by the prescribed amount. These conditions are expressed by introducing a prior distribution on the probabilities with a finite number of states, which form analogs of least-favorable configurations in the indifference zone approach. The procedure is constructed according to the first-crossing rule concept. The asymptotic properties of the sample size of the procedure are investigated. The paper concludes with numerical illustrations of the actually achievable d-posterior reliability, average sample size, and the convergence speed of the presented sample size estimates.