The curve through the expected values of order statistics with special reference to problems in nonparametric tests of hypotheses

Abstract

The expected value ot the s^th largest ot n ranked variates from a population with probability density f(x) occurs often in the statistical literature and especially in the theory of nonparametric statistics. A new expression for this value will be obtained tor any underlying density f(x) but emphasis will be placed on normal scores. A finite series representation, the individual terms of which are easy to calculate, will be obtained for the sum of squares of normal scores. The derivation of this series demonstrates a technique which can also be used to obtain the expected value of Fisher's measure or correlation as well as the expected value of the Fisher-Yates test statistic under an alternative hypothesis.