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Inequalities for variances of order statistics originating from urn models

Published online by Cambridge University Press:  24 March 2016

Krzysztof Jasiński  and
Tomasz Rychlik
Krzysztof Jasiński
Affiliation:
Nicolaus Copernicus University, Chopina 12/18, 87100 Toruń, Poland. Email address: krzys@mat.umk.pl
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Abstract

We consider the drawing with and without replacement models from numerical populations. For order statistics based on the above drawing schemes, we provide sharp upper bounds for their variances, expressed in the single observation variance units. We also characterize the populations for which the bounds are attained.

Keywords

Drawing with replacementdrawing without replacementorder statisticsvarianceoptimal bound
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 1 , March 2016 , pp. 162 - 173
Copyright
Copyright © Applied Probability Trust 2016 

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