Selection among bernoulli populations with uniformly distributed sample sizes

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.