On selecting the most likely event
In a multinomial population, when the procedure for selecting the most likely event is to choose the cell with maximum observation (ties broken by randomisation), the least favourable configuration is derived under certain restrictions on the probability vector. The results in particular disprove a conjecture of \textit{A. W. Marshall} and \textit{I. Olkin} [Inequalities: theory of majorization and its applications. (1979; Zbl 0437.26007)] and provide partial answers to all the four conjectures of \textit{R. W. Chen} and \textit{F. K. Hwang}, Commun. Stat., Theory Methods 13, 1289-1298 (1984; Zbl 0556.62017).
scientific article; zbMATH DE number 4054798