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Entropy 2012, 14(8), 1522-1538; doi:10.3390/e14081522
Article

The Entropy of a Discrete Real Variable

Received: 12 June 2012 / Revised: 3 August 2012 / Accepted: 6 August 2012 / Published: 17 August 2012
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Abstract

The discrete Shannon entropy H was formulated only to measure indeterminacy effected through a set of probabilities, but the indeterminacy in a real-valued discrete variable depends on both the allowed outcomes x and the corresponding probabilities Þ. A fundamental measure that is sensitive to both x and p is derived here from the total differential entropy of a continuous real variable and its conjugate in the discrete limit, where the conjugate is universally eliminated. The asymptotic differential entropy recovers H plus the new measure, named ≡, which provides a novel probe of intrinsic organization in sequences of real numbers.
Keywords: Shannon entropy; information entropy; information theory Shannon entropy; information entropy; information theory
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.

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Funkhouser, S. The Entropy of a Discrete Real Variable. Entropy 2012, 14, 1522-1538.

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