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The Bruss–Robertson–Steele inequality

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  13 March 2023

L. C. G. Rogers Open the ORCID record for L. C. G. Rogers [Opens in a new window]
L. C. G. Rogers*
Affiliation:
University of Cambridge
*
*Postal address: Statistical Laboratory, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB. Email: chris@statslab.cam.ac.uk
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Abstract

The Bruss–Robertson–Steele (BRS) inequality bounds the expected number of items of random size which can be packed into a given suitcase. Remarkably, no independence assumptions are needed on the random sizes, which points to a simple explanation; the inequality is the integrated form of an $\omega$-by-$\omega$ inequality, as this note proves.

Keywords

Bruss–Robertson–Steele inequalitylinear programpathwise

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 90C05: Linear programming
Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 3 , September 2023 , pp. 1112 - 1114
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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References

Bruss, F. T. (2021). The BRS-inequality and its applications. Prob. Surv. 18, 44–76.CrossRefGoogle Scholar
Bruss, F. T. and Robertson, J. B. (1991). Wald’s Lemma for sums of order statistics of IID random variables. Adv. Appl. Prob. 23, 612–623.10.2307/1427625CrossRefGoogle Scholar
Steele, J. M. (2015). The Bruss–Robertson inequality: Elaborations, extensions, and applications. Preprint, arXiv:1510.00843.Google Scholar
Whittle, P. Optimization under Constraints: Theory and Applications of Nonlinear Programming. Wiley, Chichester, 1971.Google Scholar