## The Annals of Mathematical Statistics

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

#### 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

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