On the Measurement of Randomness (Uncertainty): A More Informative Entropy
Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
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
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
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
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
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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MDPI and ACS Style
Kvålseth, T.O. On the Measurement of Randomness (Uncertainty): A More Informative Entropy. Entropy 2016, 18, 159.
Kvålseth TO. On the Measurement of Randomness (Uncertainty): A More Informative Entropy. Entropy. 2016; 18(5):159.
Kvålseth, Tarald O. 2016. "On the Measurement of Randomness (Uncertainty): A More Informative Entropy." Entropy 18, no. 5: 159.
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