Next Article in Journal
Illuminating Water and Life
Previous Article in Journal
Low-Pass Filtering Approach via Empirical Mode Decomposition Improves Short-Scale Entropy-Based Complexity Estimation of QT Interval Variability in Long QT Syndrome Type 1 Patients
Article Menu

Export Article

Open AccessArticle
Entropy 2014, 16(9), 4855-4873; doi:10.3390/e16094855

Entropy Evaluation Based on Value Validity

Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN 55455, USA
Received: 4 July 2014 / Revised: 6 August 2014 / Accepted: 18 August 2014 / Published: 5 September 2014
(This article belongs to the Section Information Theory)
View Full-Text   |   Download PDF [1047 KB, uploaded 24 February 2015]   |  

Abstract

Besides its importance in statistical physics and information theory, the Boltzmann-Shannon entropy S has become one of the most widely used and misused summary measures of various attributes (characteristics) in diverse fields of study. It has also been the subject of extensive and perhaps excessive generalizations. This paper introduces the concept and criteria for value validity as a means of determining if an entropy takes on values that reasonably reflect the attribute being measured and that permit different types of comparisons to be made for different probability distributions. While neither S nor its relative entropy equivalent S* meet the value-validity conditions, certain power functions of S and S* do to a considerable extent. No parametric generalization offers any advantage over S in this regard. A measure based on Euclidean distances between probability distributions is introduced as a potential entropy that does comply fully with the value-validity requirements and its statistical inference procedure is discussed. View Full-Text
Keywords: entropy; relative entropy; generalized entropies; entropy validity; Euclidean entropy entropy; relative entropy; generalized entropies; entropy validity; Euclidean entropy
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Kvålseth, T.O. Entropy Evaluation Based on Value Validity. Entropy 2014, 16, 4855-4873.

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