Abstract
The problem of selecting a subset of fixed size $ s $ which includes the $ t $ best of $ k $ populations $ (t leqq 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.