Selection and Ranking Procedures for Type I Extreme Value Populations and a Related Homogeneity Test

Consider k (≥2) independent Type I extreme value populations with unknown location parameters and common known scale parameter. With samples of same size, we study procedures based on the sample means for (1) selecting the population having the largest location parameter, (2) selecting the population having the smallest location parameter, and (3) testing for equality of all the location parameters. We use Bechhofer's indifference-zone and Gupta's subset selection formulations. Tables of constants for implemention are provided based on approximation for the distribution of the standardized sample mean by a generalized Tukey's lambda distribution. Examples are provided for all procedures.