Selection from Normal Populations Based on Coefficient of Variation

Abstract

In this paper two selection rules for selecting the best of k normal populations with known coefficient of variation are considered ; one is based on the sample mean and the other on sample variance. It is found that the procedure basen on variance is better than the one based on means, both in terms of smallness of minimum sample size required to achieve the given probability of correct selection and in terms of largeness of probability of correct selection. A procedure based on ML estimator is also given. The problem of selecting the best normal population when both the parameters are unknown is also considered. In this case an asymptotic solution using variance stabilising transformations is proposed.