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Selecting the Best Multinomial Cell‐Provided it is Better than a Control
Author(s) -
Chen P.
Publication year - 1988
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710300815
Subject(s) - multinomial distribution , mathematics , statistics , selection (genetic algorithm) , variance (accounting) , population , probability distribution , computer science , artificial intelligence , demography , accounting , sociology , business
Bechhofer and Turnbull (1978) considered the problems of selecting the best normal population, provided it is better than a standard for the case of known variances or equal but unknown variances. Wilcox (1984) considered the same selection goal for the case of unequal unknown variance and provided the appropriate probability equations and the necessary table. Under the same selection formulation (which we will describe formally in the following sections), this article studies a class of composite inverse sampling procedures for selecting the best multinomial cell that is better than a control cell with unknown cell probability. The procedures guarantee that (a) with probability at least P * 0 (specified), no cell is selected when the largest cell probability is sufficiently less than the control and ( b ), with probability at least P * 1 (specified), the cell with the largest probability is selected when its probability is sufficiently greater than the second largest cell probability and the control cell probability.