ON SELECTING A SUBSET WHICH INCLUDES THE $ t $ BEST OF $ k $ POPULATIONS : SCALE PARAMETER CASE

The problem of selecting a subset of fixed size s which includes the t best of k populations (t s < k), based on a pre-determined sample size n from each of the k populations, is studied as a multiple decision problem. It is assumed that the bestness of a population is characterized by its scale parameter ; the best population being the one with the largest scale parameter, and so on. Exact small and large sample methods of finding n are given for the scale parameter problem for ( i) Gamma distributions with known (possibly unequal) shape parameters (ii) Weibull distributions with known shape parameters. Some tables computed by these methods are provided. A dual problem is also discussed.