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
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 and the indifference zone . In the we insist on selecting the best for a correct selection but in the we define any selected subset to be correct if it contains the best
population. We find the least favorable configuration and the worst configuration respectively in and . We derive formulas for , and the bounds for the expected sample size . 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.