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Biometrika 1982 69(1):227-232; doi:10.1093/biomet/69.1.227
© 1982 by Biometrika Trust
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Measures of local variation in a distribution: Expected length of spacings and variances of order statistics

H. A. DAVID and R. A. GROENEVELD

Department of Statistics, Iowa State University Ames, Iowa, U.S.A

Two measures of variation about the rth order statistic Xr:n are studied: the expected value of the spacing Xr+1:n –Xr:n and the variance of Xr:n. The nature of the dependence of these measures on r, for n fixed, is examined for various classes of distributions. In the case of the variance of Xr:n the situations considered are supplemented by some asymptotic results.

Key Words: Failure rate function • Inequalities • Measure of local variation • Order statistic • Spacings


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