A Note on a Subset Selection Procedure for the Most Probable Multinomial Event

摘要

Panchapakesan (1971) proposed and investigated a subset selection procedure for selecting the most probable cell in a multinomial distribution on k ( ≥ 2) cells. He showed that the least favorable configuration (LFC) for the probability of a correct selection (PCS) is that of equal cell-probabilities. He showed that this result holds exactly for k = 2 and asymptotically for k ≥ 3. Later, Chen (1986) and Liu and Lin (1991) showed that the result holds exactly for k ≥ 3. Their proofs involve differentiation of type-2 Dirichlet integrals with the restriction that the cell-probabilities add up to unity. We now give a fairly simple proof of this result by obtaining the PCS as a single integral involving the gamma distribution. This was the proof behind the claim of the LFC result made without details in the abstract by Panchapakesan (1973).