Selection among Bernoulli populations in comparison with a standard

Abstract

In this article we consider the problem of comparing several Bernoulli populations in order to identify the population producing the largest success probability that is also larger than a given standard. We propose a fixed sample size procedure for which we develop the probability of a correct selection and the least favorable configuration. We also propose a curtailed version of the fixed sample size procedure and show that the curtailed procedure reaches the same probability of a correct selection as the fixed sample size procedure, while using fewer observations. We provide tables to implement the procedures and illustrate them via an example. We use simulations to estimate the savings by the curtailment procedure.

Keywords:

• Binomial distribution
• probability of correct selection
• ranking and selection
• sample size
• strong curtailment

SUBJECT CLASSIFICATIONS:

• 62F07
• 62L05

Acknowledgments

The author is thankful to the Editor, the Associate Editor and the referee for their time spent reading and evaluating this article, as well as for their suggestions, which led to considerable improvement in this article.