A sequential sampling rule for selecting the most probable multinomial event

Summary A sequential sampling rule is given for selecting the most probable event from a multinomial distribution withk cells. A random number of observations is taken from the given multinomial distribution at each stage of sampling, where the number is distributed according to a Poisson distribution with mean λ. The sampling is stopped when the count in any cell is greater than or equal to a given positive integerN. The cell with the highest count is selected for the most probable event. The mathematical analysis of the problem is simplified as a result of the statistical independence of the cell frequencies due to the randomization of the sample number. The expected value of the stage when the sampling terminates is decreasing in λ. The sequential sampling scheme in which one observation is taken at a time until the highest cell count is equal toN, corresponds to λ→0. A table is given showing some properties of the given selection procedure.