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

The Entropy of a Discrete Real Variable

SPAWAR Systems Center Atlantic, Joint Base Charleston, North Charleston, SC 29406, USA
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 (CC BY 3.0).
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Funkhouser, S. The Entropy of a Discrete Real Variable. Entropy 2012, 14, 1522-1538.

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