Lionnel Maugis, "Inequity Measures in Mathematical Programming for the Air Traffic Flow Management Problem with En-Route Capacities" (for IFORS 96), 1996 (CENA - Centre d'études de la Navigation Aérienne - Sofréavia, Orly Sud 205, 94542 Orly Aérogare Cedex, France) Keys: Gini, Gini index, Gini coefficient, Hoover concentration index, Coulter coefficient, Theil's entropy coefficient, Atkinson indices

#InequalityMeasures

Lionnel Maugis, "Inequity Measures in Mathematical Programming for the Air Traffic Flow Management Problem with En-Route Capacities" (for IFORS 96), 1996.

This was the first publication about inequality measures which I read before digging into this topic.

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

PS C:\Haskell> .\IneqComps.exe "0.1,7|0.9,16|9,53|40,48|50,3" IneqComps V05 2025-06-18 zGini = 69.0% (Gini index) rSym = 1.242 (symmetric Theil redundancy) zSym = 71.1% (symmetric Atkinson index, zSym = 1-exp(-rSym)) zHoover = 49.8% (Hoover index) zHappy = -0.743 (zHoover - rSym) zPlato = 70.6% (Theil equivalent ratio: 85:15)

Food for testing: IneqComps.hs computes some inequality measures. The Gini index is among them. drive.proton.me/urls/W3S6T8P... contains the executable (for the Windows shell) and source code.

#Gini #GiniIndex #EntopyMeasures #InequalityMeasures