#EntropyMeasures

Götz

@goetzkluge.bsky.social

8 months ago

Gintropy: Gini Index Based Generalization of Entropy by Tamás S. Biró [ORCID] and Zoltán Néda [ORCID] Wigner Research Centre for Physics, 1121 Budapest, Hungary Complexity Science Hub, 1080 Vienna, Austria Department of Physics, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania Author to whom correspondence should be addressed. Entropy 2020, 22(8), 879; https://doi.org/10.3390/e22080879 Submission received: 9 July 2020 / Revised: 7 August 2020 / Accepted: 8 August 2020 / Published: 10 August 2020 Abstract Entropy is being used in physics, mathematics, informatics and in related areas to describe equilibration, dissipation, maximal probability states and optimal compression of information. The Gini index, on the other hand, is an established measure for social and economical inequalities in a society. In this paper, we explore the mathematical similarities and connections in these two quantities and introduce a new measure that is capable of connecting these two at an interesting analogy level. This supports the idea that a generalization of the Gibbs–Boltzmann–Shannon entropy, based on a transformation of the Lorenz curve, can properly serve in quantifying different aspects of complexity in socio- and econo-physics. Keywords: entropy; Gini index; socio-economic inequalities; econophysics

Gintropy: Gini Index Based Generalization of Entropy
by Tamás S. Biró [ORCID] and Zoltán Néda [ORCID]

@orcid.org

#entropy #entropymeasures
#Giniindex #Ginicoefficient #Gini
#socioeconomicinequalities
#econophysics

www.mdpi.com/1099-4300/22...

Götz

@goetzkluge.bsky.social

8 months ago

Three examples for applications of IneqComps V07 2025-06-19: Source data: - Income after taxation, 1995, Germany (western part) - Source: section 20.10.4 in "Statistisches Jahrbuch 1999" - Sequence in Quantile: [taxpayers per quantile, avg.income (DM) per taxpayer] (1) -------------------------------------------------------------------------- IneqComps.exe " 1145008,2954120640| 1274868,9680072724| 1489169,18586318289|1309984,22809441408| 1227877,27624776746|1333681,36713570568|3136635,110400142095| 3619401,162869425599| 3105688,170061263504| 3252768,217925697696| 3383398,291368085566| 3126897,420417555444|207672,68629365840| 49031,32752266721|13820,18659363220| 5249,15461396661| 1247,8458445892|686,14801378844" IneqComps V07 2025-06-19 rSym = 0.39068 (symmetric Theil redundancy) zSym = 32.340% (symmetric Atkinson index, zSym = 1-exp(-rSym)) zHoover = 29.691% (Hoover index) zPlato = 42.754% (Plato inequality, Theil equivalent ratio: 71.377:28.623) zGini = 42.162% (Gini index, Gini equivalent ratio: 71.081:28.919) (2) -------------------------------------------------------------------------- IneqComps2ratios.exe "71.377,28.623|28.623,71.377" IneqComps V07 2025-06-19 rSym = 0.39067 (symmetric Theil redundancy) zSym = 32.340% (symmetric Atkinson index, zSym = 1-exp(-rSym)) zHoover = 42.754% (Hoover index) zPlato = 42.754% (Plato inequality, Theil equivalent ratio: 71.377:28.623) zGini = 42.754% (Gini index, Gini equivalent ratio: 71.377:28.623) (3) -------------------------------------------------------------------------- IneqComps.exe "71.081,28.919|28.919,71.081" IneqComps V07 2025-06-19 rSym = 0.37917 (symmetric Theil redundancy) zSym = 31.557% (symmetric Atkinson index, zSym = 1-exp(-rSym)) zHoover = 42.162% (Hoover index) zPlato = 42.162% (Plato inequality, Theil equivalent ratio: 71.081:28.919) zGini = 42.162% (Gini index, Gini equivalent ratio: 71.081:28.919)

How to use IneqComps (drive.proton.me/urls/W3S6T8P...) V07 2025-06-19:

#IncomeDistribution, #WealthDistribution, #Gini, #GiniIndex, #PlatoInequality, #TheilRedundancy, #TheilS, #HooverInequality, #inequality, #inequity, #AtkinsonIndex, #AtkinsonInequality, #EntropyMeasures, #InequalityMeasures