The Annals of Mathematical Statistics

A Single-Sample Multiple-Decision Procedure for Selecting the Multinomial Event Which Has the Highest Probability

Robert E. Bechhofer, Salah Elmaghraby, and Norman Morse

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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.

Article information

Source
Ann. Math. Statist., Volume 30, Number 1 (1959), 102-119.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177706362

Digital Object Identifier
doi:10.1214/aoms/1177706362

Mathematical Reviews number (MathSciNet)
MR105779

Zentralblatt MATH identifier
0218.62064

JSTOR
links.jstor.org

Citation

Bechhofer, Robert E.; Elmaghraby, Salah; Morse, Norman. A Single-Sample Multiple-Decision Procedure for Selecting the Multinomial Event Which Has the Highest Probability. Ann. Math. Statist. 30 (1959), no. 1, 102--119. doi:10.1214/aoms/1177706362. https://projecteuclid.org/euclid.aoms/1177706362


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