Selection Among Bernoulli Populations with Uniformly Distributed Sample Sizes

SYNOPTIC ABSTRACT

In this article we study the problem of selecting among k independent Bernoulli populations whose success probabilities are unknown, and the sample size for each population is assumed to follow a discrete uniform distribution with known range. We consider two goals and propose procedures for each goal: (1) selecting the best and (2) selecting the best in comparison with a standard. The “best” is defined as that having the highest success probability. We derive the probability of a correct selection and the least favorable configuration for each procedure by using the exact binomial distribution, without any approximation. Simulations and examples are provided to illustrate our procedures.

Key Words and Phrases::

• Bernoulli distribution
• least favorable configuration
• selection
• uniform distribution.

Acknowledgments

The authors would like to express their gratitude to the referees and the editor for their painstaking and valuable comments which made the article’s presentation clearer.