Journal of Applied Mathematics and Decision Sciences
Volume 6 (2002), Issue 1, Pages 23-42

An integrated selection formulation for the best normal mean: the unequal and unknown variance case

Pinyuen Chen1 and Jun-Lue Zhang2

1Department of Mathematics, Syracuse University, Syracuse 13244-1130, NY, USA
2Department of Mathematics, Indiana Univ. of Pennsylvania, Indian 15705- 1072, PA, USA

Copyright © 2002 Pinyuen Chen and Jun-Lue Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper considers an integrated formulation in selecting the best normal mean in the case of unequal and unknown variances. 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 (CS1) but in the IZ we define any selected subset 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 IZ. We derive formulas for P(CS1|LFC), P(CS2|WC) and the bounds for the expected sample size E(N). We also give tables for the procedure parameters to implement the proposed procedure. An example is given to illustrate how to apply the procedure and how to use the table.