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Extensions of Samuelson's Inequality |
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| Authors: | Henry Wolkowicz George P.H. Styan |
| Affiliation: | 1. Department of Mathematics , Dalhousie University , Halifax , Nova Scotia , B3H 4H8 , Canada;2. Department of Mathematics , McGill University , Montréal , Québec , H3A 2K6 , Canada |
| Abstract: | In this note we obtain upper and lower bounds for the kth largest number in a set of real numbers in terms of their mean and standard deviation. For each inequality necessary and sufficient conditions for equality are given. |
| Keywords: | Bounds for the kth largest Cauchy-Schwarz inequality Standard deviation Order statistics Inequalities Sub-sample mean |