Subset selection for the least probable multinomial cell (Q1062701)

An inverse sampling procedure R is proposed for selecting a random-size 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 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.