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Entropy 2016, 18(5), 159; doi:10.3390/e18050159

On the Measurement of Randomness (Uncertainty): A More Informative Entropy

1
Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
2
Department of Industrial & Systems Engineering, University of Minnesota, Minneapolis, MN 55455, USA
Academic Editor: Raúl Alcaraz Martínez
Received: 11 February 2016 / Revised: 7 April 2016 / Accepted: 15 April 2016 / Published: 26 April 2016
(This article belongs to the Section Information Theory)
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Abstract

As a measure of randomness or uncertainty, the Boltzmann–Shannon entropy H has become one of the most widely used summary measures of a variety of attributes (characteristics) in different disciplines. This paper points out an often overlooked limitation of H: comparisons between differences in H-values are not valid. An alternative entropy H K is introduced as a preferred member of a new family of entropies for which difference comparisons are proved to be valid by satisfying a given value-validity condition. The H K is shown to have the appropriate properties for a randomness (uncertainty) measure, including a close linear relationship to a measurement criterion based on the Euclidean distance between probability distributions. This last point is demonstrated by means of computer generated random distributions. The results are also compared with those of another member of the entropy family. A statistical inference procedure for the entropy H K is formulated. View Full-Text
Keywords: randomness; uncertainty; entropy; value validity randomness; uncertainty; entropy; value validity
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Kvålseth, T.O. On the Measurement of Randomness (Uncertainty): A More Informative Entropy. Entropy 2016, 18, 159.

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