Inverse sampling subset selection of multinomial cells

A subset selection procedure R is proposed for selecting a subset which includes the t “best” cells (i.e., cells with the t largest cell probabilities) from a multinomial distribution with k cells (1 ≤ t ≤ k). Procedure R uses inverse sampling; the measure of distance is the ratio of the cell probabilities. Type-2 Dirichlet integrals are used (i) to express the probability of a correct selection in terms of integrals with parameters only in the upper or lower limits of integration, and (ii) to prove that (under a condition on the parameter space) the least-favorable configuration for R is the so-called slippage configuration with k equal cell probabilities.