Distribution theory for selection from logistic populations

Assume k (integer k \geq 2) independent populations \pi_1, \pi_2, ..., \pi_k are given. The associated independent random variables X_1, X_2, ..., X_k are Logistically distributed with unknown means \mu_1, \mu_2, ..., \mu_k, respectively, and common known variance. The goal is to select the best population, this is the population with the largest mean. Some distributional results are derived for subset selection as well as for the indifference zone approach. The probability of correct selection is determined. Exact and numerical results concerning the expected subset size are presented for the subset selection approach. Finally, some remarks are made for a generalized selection goal using subset selection. This goal is to select a non-empty subset of populations that contains at least one \epsilon-best (almost best) treatment with confidence level P*. For a set of populations an \epsilon-best reatment is defined as a treatment with location parameter on a distance less than or equal to \epsilon (\epsilon \geq 0) from the best population