An integrated selection formulation for the best normal mean: the unequal and unknown variance caseReport as inadecuate




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



Department of Mathematics, Syracuse University, Syracuse 13244-1130, NY, USA

Department of Mathematics, Indiana Univ. of Pennsylvania, Indian 15705- 1072, PA, USA



Copyright © 2002 Hindawi Publishing Corporation. 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.

Abstract

This paper considers an integrated formulation in selecting the best normalmean in the case of unequal and unknown variances. The formulation separates theparameter 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 bestpopulation. We find the least favorable configuration LFC and the worst configuration WC respectively in PZ and IZ. We derive formulas for PCS1|LFC, PCS2|WC and the bounds for the expected sample size EN. 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.





Author: Pinyuen Chen and Jun-Lue Zhang

Source: https://www.hindawi.com/



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