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The American Statistician Volume 42, 1988 - Issue 3
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Teacher's Corner

The Monotonicity of Power Means Using Entropy

D. R. Shier Department of Mathematics, College of William and Mary, Williamsburg, Virginia, 23185, USA
Pages 203-204 | Received 01 Mar 1987, Published online: 27 Feb 2012
 
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Abstract

The arithmetic-geometric-harmonic mean inequalities are special cases of a more general result concerning the monotonicity of power means. This note identifies a relationship with the entropy of a probabilistic system, and thereby provides an alternative and elementary derivation of this monotonicity result.

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