Maximization of statistical heterogeneity: From Shannon’s entropy to Gini’s index

Iddo Eliazar and Igor M. Sokolov

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 16, 3023-3038

Abstract: Different fields of Science apply different quantitative gauges to measure statistical heterogeneity. Statistical Physics and Information Theory commonly use Shannon’s entropy which measures the randomness of probability laws, whereas Economics and the Social Sciences commonly use Gini’s index which measures the evenness of probability laws. Motivated by the principle of maximal entropy, we explore the maximization of statistical heterogeneity–for probability laws with a given mean–in the four following scenarios: (i) Shannon entropy maximization subject to a given dispersion level; (ii) Gini index maximization subject to a given dispersion level; (iii) Shannon entropy maximization subject to a given Gini index; (iv) Gini index maximization subject to a given Shannon entropy. Analysis of these four scenarios results in four different classes of heterogeneity-maximizing probability laws–yielding an in-depth description of both the marked differences and the interplay between the Physical “randomness-based” and the Economic “evenness-based” approaches to the maximization of statistical heterogeneity.

Keywords: Statistical heterogeneity; Dispersion; Entropy; Egalitarianism; Shannon’s entropy; Gini’s index; Subbotin’s distribution; The logistic distribution (search for similar items in EconPapers)
Date: 2010
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437110002906
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:16:p:3023-3038

DOI: 10.1016/j.physa.2010.03.045

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().