On Ranking Parameters of Scale in Type III Populations

Abstract

The problem is considered of selecting, from a given set of Type III populations with unknown scale parameters, a subset which is most likely to contain the population having the largest or smallest scale parameter, with the help of a decision rule which ensures many desirable properties. An infinite class of decision rules is shown to possess a majority of these desirable properties but among this class only one rule is considered to be optimum in the sense that it alone will usually minimize the expected size of the selected subset. The optimum rule is shown to depend on the extreme order statistic. The usefulness of this problem is illustrated by a few examples. * This paper was presented at the 43rd Session of the Indian Science Congress Association held in 1956.