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

[摘要] 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 thePZwe insist on selecting the best for a correct selection(CS1)but in theIZwe 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 inPZandIZ. We derive formulas forP(CS1|LFC),P(CS2|WC)and the bounds for the expected sample sizeE(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.

[学科分类] 自然科学（综合）