Selecting the best population: A decision theoretic approach: The case of Pareto distribution

Abstract

The main ideas in selecting the best populations meeting some prescribed optimality criterion have been mooted originally by Bechchofer and Gupta and the subject has gone from strength to strength by several contributions by several statisticians over the last three decades. In this paper, the selection problem is tackled from a decision theoretic point of view. In selecting the best population, we take into account the cost of sampling and the penalties for taking a wrong decision. We are basically interested in selecting the best Pareto population following the lead given by Somerville and Ofosu. The Pareto proposed this model to study the distribution of incomes in various societies for comparison. In medical circles, this has been used as a model for the remission rate of discharged psychiatric patients as a survival model for cardiac patients waiting for a heart transplant operation. This paper considers four different types of penalty functions including the one considered by Ofosu. Under three of these penalty function we derive the minimax sample sizes. The maximum of the resultant loss function is explicitly derived overcoming the difficulty faced by Ofosu