ON USING A LOSS FUNCTION IN SELECTING THE BEST OF 2 GAMMA-POPULATIONSIN TERMS OF THEIR SCALE-PARAMETERS

This paper continues the study of the subset selection procedure propo sed by van der Laan and van Eeden [1]. In that paper the authors consi der a location problem and base their procedure on a continuous loss f unction. This loss function takes into account the ''distance'', in pa rameter values, between the populations under consideration and the be st one among the ones in the selected subset. In defining this ''dista nce'', they incorporate the notion of ''epsilon-best'' studied by, e.g ., Desu [2], Lam [3], van der Laan [4], Gill and Sharma [5] and Gill, Sharma and Misra [6]. As an example of their results, van der Laan and van Eeden [1] consider the case of two normal populations with equal known variances. The present paper develops a similar procedure for sc are parameters. The case of two gamma populations with equal known sha pe parameters is studied in detail.