A Two-Stage Procedure for Selecting the Population with the Largest Mean when Common Variance Is Unknown

In this paper, the technique to select the population associated with the largest mean from k populations with unknown locations and a common unknown scale parameter is investigated. Asymptotic approximations to the distribution of the linear combination of the sample mean and the sample standard deviation has been derived. Using this approximation, an elimination type of two-stage procedure is proposed. Furthermore, two lower bounds on the probability of correct selection are obtained. This procedure are applied to the logistic population in detail.