Next Article in Journal
Optimization of Two-Stage Peltier Modules: Structure and Exergetic Efficiency
Previous Article in Journal
Potential and Evolution of Compressed Air Energy Storage: Energy and Exergy Analyses
Article Menu

Export Article

Open AccessArticle
Entropy 2012, 14(8), 1522-1538; https://doi.org/10.3390/e14081522

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
Full-Text   |   PDF [374 KB, uploaded 24 February 2015]   |  

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. View Full-Text
Keywords: Shannon entropy; information entropy; information theory Shannon entropy; information entropy; information theory
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

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

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top