Wealth distribution in the US, 1990: X:\Haskell> .\IneqComps.exe "50,2.36|40,37.8|9,41.7|0.9,12.6|0.1,5.51" IneqComps V16 2025-06-25 rSym = 1.24162 (symmetric Theil redundancy) zSym = 71.108% (symmetric Atkinson inequality, zSym=1-exp(-rSym)) zPlato = 70.605% (Plato inequality, Theil & Atkinson & Plato equivalent ratio: 85.303:14.697) zGini = 69.040% (Gini inequality, Gini equivalent ratio: 84.520:15.480) zHoover = 49.828% (Hoover inequality, Hoover equivalent ratio: 74.914:25.086) 1-Median = 92.121% zAccept = -0.74334 (experimental: zAccept=zHoover-rSym) Wealth distribution in the US, 2020: PS X:\Haskell> .\IneqComps.exe "50,2.385|40,28.9|9,37.7|0.9,16.7|0.1,14.3" IneqComps V16 2025-06-25 rSym = 1.53123 (symmetric Theil redundancy) zSym = 78.373% (symmetric Atkinson inequality, zSym=1-exp(-rSym)) zPlato = 76.302% (Plato inequality, Theil & Atkinson & Plato equivalent ratio: 88.151:11.849) zGini = 74.734% (Gini inequality, Gini equivalent ratio: 87.367:12.633) zHoover = 58.710% (Hoover inequality, Hoover equivalent ratio: 79.355:20.645) 1-Median = 94.466% zAccept = -0.94413 (experimental: zAccept=zHoover-rSym)

Whoops, the previous post was about 1990 (left side), not 2020 (right side).

#TheilIndex #TheilRedundancy #AtkinsonInequality #PlatoInequality #Gini #GiniIndex #GiniCoefficiant #HooverInequality #HooverIndex

Here are some wealth inequality indicators, this time for 1990 and 2020:

Graph depicting the "Distribution of Household Wealth in the U.S. by income group" groups: [0%,50%), group size 50% [0%,90%), group size 40% [90%,99%), group size 39% [99%,99.9%), group size 0.9% [99%.9%,100%], group size: 0.1% time range: 1990-2020 (or later?) Source: The Federal Reserve ----------------------------------------------------------- Processed in Power Shell: X:\Haskell> .\IneqComps.exe "50,2.36|40,37.8|9,41.7|0.9,12.6|0.1,5.51" IneqComps V16 2025-06-25 rSym = 1.24162 (symmetric Theil redundancy) zSym = 71.108% (symmetric Atkinson inequality, zSym=1-exp(-rSym)) zPlato = 70.605% (Plato inequality, Theil & Atkinson & Plato equivalent ratio: 85.303:14.697) zGini = 69.040% (Gini inequality, Gini equivalent ratio: 84.520:15.480) zHoover = 49.828% (Hoover inequality, Hoover equivalent ratio: 74.914:25.086) 1-Median = 92.121% zAccept = -0.74334 (experimental: zAccept=zHoover-rSym) X:\Haskell> .\IneqComps.exe --CSV "50,2.36|40,37.8|9,41.7|0.9,12.6|0.1,5.51" 1.241620979176E+00;711.084487868371E-03;706.052940093059E-03;690.396018805642E-03;498.279483845153E-03;921.205035971223E-03;-743.341495331143E-03;+1.000000000000E+00

Any city however small, is divided at least into two, one the city of the poor, the other of the rich; these are hostile to each other. (Plato, Politeia, 370 BC) In the following example are five "cities". The redundancy (that's maximum entropy minus measured entropy) of the 4 cities is similar to the redundancy of the wealth distribution in two cities, where - in the poor city 85.303% of the people own 14.697% of the wealth, and - in the rich city 14.697% of the people own 85.303% of the wealth. The Plato inequality indicator has been developed to get the data required for such a statement. In the mid inequality range, the The Plato inequality indicator behaves pretty much like the Plato inequality indicator, but in the high inequality renge it is more sensitive then the Gini. X:\Haskell> .\IneqComps.exe "50,2.36|40,37.8|9,41.7|0.9,12.6|0.1,5.51" IneqComps V16 2025-06-25 rSym = 1.24162 (symmetric Theil redundancy) zSym = 71.108% (symmetric Atkinson inequality, zSym=1-exp(-rSym)) zPlato = 70.605% (Plato inequality, Theil & Atkinson & Plato equivalent ratio: 85.303:14.697) zGini = 69.040% (Gini inequality, Gini equivalent ratio: 84.520:15.480) zHoover = 49.828% (Hoover inequality, Hoover equivalent ratio: 74.914:25.086) 1-Median = 92.121% zAccept = -0.74334 (experimental: zAccept=zHoover-rSym) X:\Haskell> .\IneqComps.exe --CSV "50,2.36|40,37.8|9,41.7|0.9,12.6|0.1,5.51" 1.241620979176E+00;711.084487868371E-03;706.052940093059E-03;690.396018805642E-03;498.279483845153E-03;921.205035971223E-03;-743.341495331143E-03;+1.000000000000E+00

Computing inequality indicators (Theil, Atkinson, Plato, Gini, Hoover) for the wealth distribution in the US, 2020 (right side of the graph).

#TheilIndex #TheilRedundancy #AtkinsonInequality #PlatoInequality #Gini #GiniIndex #GiniCoefficiant #HooverInequality #HooverIndex

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