## The Annals of Mathematical Statistics

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

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

Robert E. Bechhofer, Salah Elmaghraby, and Norman Morse

#### 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