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The Monotonicity of Power Means Using Entropy

D. R. Shier
The American Statistician
Vol. 42, No. 3 (Aug., 1988), pp. 203-204
DOI: 10.2307/2685004
Stable URL: http://www.jstor.org/stable/2685004
Page Count: 2
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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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