An integrated formulation for selecting the best normal population: the common and unknown variance case

Abstract

This paper considers an integrated formulation in selecting the best normal means in the case of common and unknown variance. The formulation separates the parameter space into two disjoint parts, the preference zone (PZ) and the indifference zone (IZ). In the PZ we insist on selecting the best for a correct selection (CSi) but in the IZ we define any selected subet to be correct (CS2) if it contains the best population. We find the least favorable configuration (LFC) and the worst configuration (WC) respectively in PZ and in the entire parameter space. We derive formulas for P(CSi|LFC), P(CS2|WC), and the bounds for the expected sample size E(N). We also provide tables for the procedure parameters to implement the proposed procedure. An example is given to illustrate the procedure and the table.