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2017 Variance and the inequality of arithmetic and geometric means
Burt Rodin
Rocky Mountain J. Math. 47(2): 637-648 (2017). DOI: 10.1216/RMJ-2017-47-2-637

Abstract

A number of recent papers have been devoted to generalizations of the classical AM-GM inequality. Those generalizations which incorporate \textit {variance} have been the most useful in applications to economics and finance. In this paper, we prove an inequality which yields the best possible upper and lower bounds for the geometric mean of a sequence solely in terms of its arithmetic mean and its variance. A particular consequence is the following: among all positive sequences having given length, arithmetic mean and nonzero variance, the geometric mean is maximal when all terms in the sequence except one are equal to each other and are less than the arithmetic mean.

Citation

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Burt Rodin. "Variance and the inequality of arithmetic and geometric means." Rocky Mountain J. Math. 47 (2) 637 - 648, 2017. https://doi.org/10.1216/RMJ-2017-47-2-637

Information

Published: 2017
First available in Project Euclid: 18 April 2017

zbMATH: 1370.26062
MathSciNet: MR3635378
Digital Object Identifier: 10.1216/RMJ-2017-47-2-637

Subjects:
Primary: 26D07

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 2 • 2017
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