TRUNCATED SELECTION PROCEDURES FOR THE MOST PROBABLE EVENT AND THE LEAST PROBABLE EVENT

PINYUEN CHEN

Department of Mathematics, Syracuse University, Syracuse, NY 13244-1150, U.S.A.

(Received November 6, 1989; revised September 30, 1991)

Abstract. This paper proposes two sequential procedures for selecting respectively the multinomial cell with the largest cell probability and the multinomial cell with the smallest cell probability. The stopping rule for both procedures uses truncation of the procedure studied by Ramey and Alam (1979, Biometrika, 66, 171–173). A property of the least favorable configuration of the proposed procedures is proved, which partially solves a conjecture given in Ramey and Alam (1979). The proposed procedures are compared with other procedures which have been considered in the literature and are found to be better in certain respects.

Key words and phrases: Multinomial distribution, ranking, selection.