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INEQUALITIES CONCERNING THE EXPECTED

SELECTION DIFFERENTIALS

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

^{1} *Department of Mathematics, University of Leicester, University Road, Leicester, U.K.*

^{2} *Department 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.

**Source**
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