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Entropy 2014, 16(9), 4855-4873;

Entropy Evaluation Based on Value Validity

Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
Received: 4 July 2014 / Revised: 6 August 2014 / Accepted: 18 August 2014 / Published: 5 September 2014
(This article belongs to the Section Information Theory)
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Besides its importance in statistical physics and information theory, the Boltzmann-Shannon entropy S has become one of the most widely used and misused summary measures of various attributes (characteristics) in diverse fields of study. It has also been the subject of extensive and perhaps excessive generalizations. This paper introduces the concept and criteria for value validity as a means of determining if an entropy takes on values that reasonably reflect the attribute being measured and that permit different types of comparisons to be made for different probability distributions. While neither S nor its relative entropy equivalent S* meet the value-validity conditions, certain power functions of S and S* do to a considerable extent. No parametric generalization offers any advantage over S in this regard. A measure based on Euclidean distances between probability distributions is introduced as a potential entropy that does comply fully with the value-validity requirements and its statistical inference procedure is discussed. View Full-Text
Keywords: entropy; relative entropy; generalized entropies; entropy validity; Euclidean entropy entropy; relative entropy; generalized entropies; entropy validity; Euclidean entropy
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Kvålseth, T.O. Entropy Evaluation Based on Value Validity. Entropy 2014, 16, 4855-4873.

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