Classifying logistic populations using sample medians

Consider k(⩾2)k(⩾2) independent populations π1,…,πkπ1,…,πk such that an observation from population πiπi follows a logistic distribution with unknown location parameter μiμi and common known scale parameter σ2,i=1,…,kσ2,i=1,…,k. Let μ[1]⩽⋯⩽μ[k]μ[1]⩽⋯⩽μ[k] be the unknown ordered values of μμs and the population associated with μ[k]μ[k] be the upper extreme population (UEP) and the population associated μ[1]μ[1] be the lower extreme population (LEP). In this paper, we discuss a procedure on the lines of Liu [On a multiple three-decision procedure for comparing several treatments with a control. Austral. J. Statist. 39, 79–97] and Boher [Multiple three-decision rules for parametric signs. J. Amer. Statist. Assoc. 74, 432–437], for classifying k   logistic populations by the location parameters as better or worse than a control/standard population. In the absence of any standard/control population, we propose a selection procedure for simultaneous selection of two non-empty random size subsets, one containing population associated with largest mean and the other containing population associated with smallest mean with a pre-specified probability P*(1/k(k-1)