INEQUALITIES CONCERNING THE EXPECTED SELECTION DIFFERENTIALS

BRIAN J. ENGLISH^{1}, RAPHAEL GILLETT^{2} AND MICHAEL J. PHILLIPS^{1}

1Department of Mathematics, University of Leicester, University Road, Leicester, U.K. 2Department of Psychology, University of Leicester, University Road, Leicester, U.K.

(Received January 12, 1990; revised October 8, 1990)

Abstract. In many situations two populations are compared on the basis of subsets of the available data. If this is done using the same fraction of “best” records, then the expectations of the arithmetic means of these fractions are strictly ordered in magnitude by the ordering of the sample sizes. The results are illustrated with the special cases of the uniform and negative exponential distributions, for which further inequalities are derived.

Key words and phrases: Order statistics, means of extreme subsets, inequalities.