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March, 1959 A Single-Sample Multiple-Decision Procedure for Selecting the Multinomial Event Which Has the Highest Probability
Robert E. Bechhofer, Salah Elmaghraby, Norman Morse
Ann. Math. Statist. 30(1): 102-119 (March, 1959). DOI: 10.1214/aoms/1177706362

Abstract

The problem of selecting the multinomial event which has the highest probability is formulated as a multiple-decision selection problem. Before experimentation starts the experimenter must specify two constants $(\theta^{\ast}, P^{\ast})$ which are incorporated into the requirement: "The probability of a correct selection is to be equal to or greater than $P^{\ast}$ whenever the true (but unknown) ratio of the largest to the second largest of the population probabilities is equal to or greater than $\theta^{\ast}$." A single-sample procedure which meets the requirement is proposed. The heart of the procedure is the proper choice of $N$, the number of trials. Two methods of determining $N$ are described: the first is exact and is to be used when $N$ is small; the second is approximate and is to be used when $N$ is large. Tables and sample calculations are provided.

Citation

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Robert E. Bechhofer. Salah Elmaghraby. Norman Morse. "A Single-Sample Multiple-Decision Procedure for Selecting the Multinomial Event Which Has the Highest Probability." Ann. Math. Statist. 30 (1) 102 - 119, March, 1959. https://doi.org/10.1214/aoms/1177706362

Information

Published: March, 1959
First available in Project Euclid: 27 April 2007

zbMATH: 0218.62064
MathSciNet: MR105779
Digital Object Identifier: 10.1214/aoms/1177706362

Rights: Copyright © 1959 Institute of Mathematical Statistics

Vol.30 • No. 1 • March, 1959
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