Subset selection for the least probable multinomial cell

An inverse sampling procedure R is proposed for selecting a randomsize subset which contains the least probable cell (i.e., the cell with the smallest cell probabilities) from a multinomial distribution with k cells. Type 2-Dirichlet integrals are used (i) to express the probability of a correct selection in terms of integrals with parameters only in the limits of integration, (ii) to prove that the least favorable configuration under R is the so-called slippage configuration with k equal cell probabilities, and (iii) to express exactly the expectation of the total number of observations required and the expectation of the subset size under the procedure R.