An Integrated Formulation for Selecting the Best From Several Normal Populations in Terms of the Absolute Values of Their Means: Common Known Variance Case
Sakthivel Jeyaratnam, Shanker Shyam S. Panchapakesan · Birkhäuser Boston eBooks · 1997
Consider k (≥ 2) normal populations with unknown means μ i (i = 1,…,k) and known common variance σ 2. Let θ i = |μ i |. Rizvi (1971) investigated the problem of selecting the population associated with the largest θ i under the indifference zone approach of Bechhofer (1954) and the subset selection approach of Gupta (1956, 1965). We consider here an integrated formulation of the problem combining features of the two classical approaches. For the proposed procedure we establish the form of the least favorable configurations over the indifference zone and the preference zone, and obtain results regarding determination of the sample size and constants associated with the procedure in order to guarantee minimum probability of correct decision for each zone. Properties of some operating characteristics are also studied.