Next Article in Journal
Ensemble Averages, Soliton Dynamics and Influence of Haptotaxis in a Model of Tumor-Induced Angiogenesis
Next Article in Special Issue
Improving the Naive Bayes Classifier via a Quick Variable Selection Method Using Maximum of Entropy
Previous Article in Journal
Objective Bayesian Entropy Inference for Two-Parameter Logistic Distribution Using Upper Record Values
Previous Article in Special Issue
Entropy “2”-Soft Classification of Objects
Article Menu
Issue 5 (May) cover image

Export Article

Open AccessArticle
Entropy 2017, 19(5), 204; doi:10.3390/e19050204

Measures of Qualitative Variation in the Case of Maximum Entropy

1
Department of Statistics, Yildiz Technical University, 34220 Istanbul, Turkey
2
Department of Informatics, Marmara University, 34180 Istanbul, Turkey
*
Author to whom correspondence should be addressed.
Academic Editor: Dawn E. Holmes
Received: 13 March 2017 / Revised: 21 April 2017 / Accepted: 27 April 2017 / Published: 4 May 2017
(This article belongs to the Special Issue Maximum Entropy and Its Application II)
View Full-Text   |   Download PDF [906 KB, uploaded 4 May 2017]   |  

Abstract

Asymptotic behavior of qualitative variation statistics, including entropy measures, can be modeled well by normal distributions. In this study, we test the normality of various qualitative variation measures in general. We find that almost all indices tend to normality as the sample size increases, and they are highly correlated. However, for all of these qualitative variation statistics, maximum uncertainty is a serious factor that prevents normality. Among these, we study the properties of two qualitative variation statistics; VarNC and StDev statistics in the case of maximum uncertainty, since these two statistics show lower sampling variability and utilize all sample information. We derive probability distribution functions of these statistics and prove that they are consistent. We also discuss the relationship between VarNC and the normalized form of Tsallis (α = 2) entropy in the case of maximum uncertainty. View Full-Text
Keywords: maximum entropy; measures of qualitative variation; VarNC statistic; StDev statistic; Tsallis entropy; power-divergence statistic maximum entropy; measures of qualitative variation; VarNC statistic; StDev statistic; Tsallis entropy; power-divergence statistic
Figures

Figure 1

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).

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

Evren, A.; Ustaoğlu, E. Measures of Qualitative Variation in the Case of Maximum Entropy. Entropy 2017, 19, 204.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

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