Inverse-Type Sampling Procedure for Estimating the Number of Multinomial Classes

摘要

A procedure with inverse-type sampling is proposed for the estimation of the number of classes (or cells) in a given multinomial distribution with a devised stopping rule that satisfies a preassigned P~* condition and controls the probability of a correct decision P{CD}. Dirichlet Integrals of Type Ⅱ are adapted for developing the procedure, which is based on a decision-theoretic approach. We assume that we know neither the number of classes (or cells) nor the cell probabilities (parameters) of the given multinomial but we do assume the minimum cell probability ε(>0). Finally, the Monte Carlo experimentation is carried out in order to illustrate the theoretical results and the behavior of proposed procedure.