Wie ungleich sind Einkommen in Europa verteilt? (Statista + Zusatzinfos + Kurzkommentar) Briefing Wirtschaft, Economy, Einkommen, Ungleichheit, Gini-Index, Einkommens-Gini, Vermögens-Gini, Income, Fortune, Asset Wir arbeiten weiter an der Vermessung der Gesellschaft nach ökonomischen G…

Wie ungleich sind Einkommen in Europa verteilt? (Statista + Zusatzinfos + Kurzkommentar) #GiniKoeffizient #GiniIndex #Einkommen #Vermögen #Income #Asset #Economy #Wirtschaft #Einkommensungleichheit #Ungleichheit #Vermögensungleichheit #EU #Germany

derwahlberliner.com/2025/12/02/w...

US outclasses Europe in GDP. Does this mean that americans are better off? #giniindex TypeAshton youtu.be/eiymTzsZfoA?...

Gini index serves as an essential tool for assessing income inequality within a country by examining how income is distributed among its people. #finsurlog #finance #Giniindex
Read more at: finsurlog.com/what-is-gini...

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Railways to Begin Chart Preparation 8 Hours Before Departure Starting Now!
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#railways #IndiaRising #GiniIndex #EconomicEquality #InclusiveGrowth #IndiaDevelopment #WorldBankStats #IncomeEquality #Sakshamagarwal #india#news

T = rSym = (Theil_T[(a,b)] + Theil_T[(a,b)]) / 2 H = zHoover = Hoover inequality ("Robin Hood index") Software to compute theses measures: in https://drive.proton.me/urls/FBYNTG45P4#RafOE8CV1KPf The original source: TheilHooverPlatoGini.hs (Haskell code). I additionally generated TheilHooverPlatoGini.py and TheilHooverPlatoGini.lua using ChatGPT.

Plato_Inequality_Indicator.hs (Haskell code) is here: in https://drive.proton.me/urls/FBYNTG45P4#RafOE8CV1KPf You can use e.g. GhatGPT to convert the code to other languages.

Two experimental inequality measures:
- zPlato
- rAccept and zAccept

The acceptance measure surely is disputable.

#ResearchProposal #TheilIndex #TheilRedundancy #HooverInequality #HooverIndex #RobinHoodIndex #Gini #GiniIndex #GiniCoefficient #PlatoInequality #inequality

See also ALT-text

-- Part 1 -- -- This Haskell code was sent as a prompt to Meta AI: -- Request to Meta AI: -- Not considering computation errors, -- show that both functions are equivalent. -- --------------------------------------------------------------------------------- type GroupSize = Double type GroupRessources = Double type Percentile = (GroupSize, GroupRessources) type AllPercentiles = [Percentile] type Percentiles = [(GroupSize, GroupRessources)] type TheilRedundancy = Double computeTheilT_1 :: Percentiles -> TheilRedundancy computeTheilT_1 allPercentiles = 0.5 * sum [log (a / b) * ((a / aTotal) - (b / bTotal)) | (a, b) <- allPercentiles] where aTotal = sum [a | (a, _) <- allPercentiles] bTotal = sum [b | (_, b) <- allPercentiles] computeTheilT_2 :: Percentiles -> TheilRedundancy computeTheilT_2 allPercentiles = 0.5 * sum [theilTab a b aTotal + theilTba a b bTotal | (a, b) <- allPercentiles] where aTotal = sum [a | (a, _) <- allPercentiles] bTotal = sum [b | (_, b) <- allPercentiles] theilTab a b aTotal = a * log (a / b) / aTotal theilTba a b bTotal = b * log (b / a) / bTotal -- --------------------------------------------------------------------------------- main :: IO () main = do let percentiles = [(10, 10), (20, 400), (30, 9000), (40, 160000)] let theilT_1 = computeTheilT_1 percentiles let theilT_2 = computeTheilT_2 percentiles print ("Theil T (1): " ++ show theilT_1) print ("Theil T (2): " ++ show theilT_2) {- > .\SymmetricTheilT.exe "Theil T (1): 1.2577697898110196" "Theil T (2): 1.2577697898110196" -}

-- Part 2 -- main :: IO () main = do let percentiles = [(10, 10), (20, 400), (30, 9000), (40, 160000)] let theilT_1 = computeTheilT_1 percentiles let theilT_2 = computeTheilT_2 percentiles print ("Theil T (1): " ++ show theilT_1) print ("Theil T (2): " ++ show theilT_2) {- > .\SymmetricTheilT.exe "Theil T (1): 1.2577697898110196" "Theil T (2): 1.2577697898110196" -} {- Answer from Meta AI: Let's expand theilTab a b aTotal + theilTba a b bTotal: theilTab a b aTotal + theilTba a b bTotal = a * log (a / b) / aTotal + b * log (b / a) / bTotal = a * (log a - log b) / aTotal + b * (log b - log a) / bTotal = a * log a / aTotal - a * log b / aTotal + b * log b / bTotal - b * log a / bTotal = log a * (a / aTotal - b / bTotal) - log b * (a / aTotal - b / bTotal) = (log a - log b) * (a / aTotal - b / bTotal) = log (a / b) * (a / aTotal - b / bTotal) This is equivalent to the expression in computeTheilT_1. Therefore, both functions are equivalent. The output of your program also confirms this, as both theilT_1 and theilT_2 have the same value. -}

Symmetrized Theil-T Redundancy:

½ (a * ln (a / b) / aTotal + b * ln (b / a) / bTotal)

and

½ ln (a / b) * (a / aTotal - b / bTotal)

are equivalent.

#Theilindex #TheilRedundancy #GiniIndex #Ginicoefficient

Computing inequality measures:
snrk.de/TheilHooverP... contains Haskell code for computing the following symmetric (swap-invariant) #inequality indicators:
※ Gini [0,1]
※ Hoover [0,1]
※ Plato [0,1]
※ Theil_sym [0,∞), Theil_symCDF [0,1]

#Giniindex, #Gini, #Theilindex, #Platoinequality, #Hooverindex

Data source: https://www.federalreserve.gov/releases/z1/dataviz/dfa/distribute/chart/#range:1990.3,2024.4;quarter:142;series:Net%20worth;demographic:income;population:all;units:levelshttps://www.federalreserve.gov/releases/z1/dataviz/dfa/distribute/chart/#range:1990.3,2024.4;quarter:142;series:Net%20worth;demographic:networth;population:all;units:levels Wealth Distribution (Grouping: Wealth per Wealth Percentile) 20,20,20,20,19,1 Year|Plato|Gini 1990|67.36%|65.92% 1991|67.14%|65.65% 1992|66.48%|65.11% 1993|67.21%|65.51% 1994|68.06%|65.89% 1995|68.23%|65.89% 1996|68.62%|66.18% 1997|68.95%|66.57% 1998|69.27%|66.98% 1999|69.45%|67.41% 2000|69.39%|67.52% 2001|68.91%|67.01% 2002|69.01%|67.08% 2003|69.83%|67.70% 2004|70.83%|68.51% 2005|71.19%|68.83% 2006|72.00%|69.51% 2007|73.60%|70.60% 2008|75.77%|71.52% 2009|78.59%|72.38% 2010|80.18%|73.19% 2011|81.04%|73.52% 2012|79.99%|73.41% 2013|78.61%|73.11% 2014|77.92%|73.21% 2015|77.56%|73.26% 2016|77.02%|73.13% 2017|76.43%|72.99% 2018|75.74%|72.76% 2019|75.37%|72.66% 2020|73.97%|71.38% 2021|73.58%|70.81% 2022|72.37%|69.48% 2023|72.69%|69.71% 2024|73.06%|70.00%

https://www.federalreserve.gov/releases/z1/dataviz/dfa/distribute/chart/#range:1990.3,2024.4;quarter:142;series:Net%20worth;demographic:income;population:all;units:levels Wealth Distribution (Grouping: Wealth per Income Percentile) year|Plato|Gini 1990|42.51%|39.19% 1991|42.91%|39.32% 1992|42.84%|39.27% 1993|43.66%|39.73% 1994|43.96%|39.61% 1995|44.88%|39.78% 1996|45.57%|40.44% 1997|46.50%|41.41% 1998|47.60%|42.64% 1999|48.05%|43.82% 2000|48.24%|44.77% 2001|46.69%|44.13% 2002|46.37%|43.47% 2003|47.35%|43.37% 2004|50.07%|44.43% 2005|51.24%|45.46% 2006|52.68%|46.94% 2007|54.07%|48.42% 2008|52.48%|47.88% 2009|50.52%|47.23% 2010|51.07%|48.40% 2011|52.11%|49.52% 2012|53.18%|50.46% 2013|54.57%|51.61% 2014|55.97%|52.87% 2015|56.60%|53.48% 2016|56.98%|53.76% 2017|57.53%|53.95% 2018|57.60%|53.67% 2019|57.87%|53.64% 2020|56.56%|52.85% 2021|57.28%|53.58% 2022|55.18%|51.88% 2023|55.50%|52.28% 2024|56.48%|53.19%

USA 1990 - 2024

The inequality of wealth distribution over wealth percentiles devreased from 2011 to 2024.

The inequality of wealth distribution over income percentiles increased.

Data Source: FED (Links in ALT-Text)

Indicators #Gini #Giniindex #Platoinequality

dfa-networth-levels_fromIneqComps.xlsx See https://drive.proton.me/urls/VW05METQ2G#fWlnSQkKhSvY

Wealth distribution: https://www.federalreserve.gov/releases/z1/dataviz/dfa/distribute/chart/#range:1989.3,2025.1;quarter:142;series:Net%20worth;demographic:networth;population:all;units:levels

Inequality measures for the distribution of wealth (net-worth) in the USA from 1990 to 2024.

See also: drive.proton.me/urls/VW05MET...

#inequality #wealthinequality #wealthdistribution #incomeinequality #incomedistribution #Gini #Giniindex #Platoinequality

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...

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

# Example in Python for how to compute the Plato inequality indicator: # Goetz Kluge, 2025-06-25 import math # Compute rSym (symmetrized Theil redundancy) from a table of pairs (a,b). def compute_theil_redundancy(pairs): a_total = sum(a for a, _ in pairs) b_total = sum(b for _, b in pairs) return 0.5 * sum(math.log(a / b) * ((a / a_total) - (b / b_total)) for a, b in pairs) def theil2atkinson(redundancy): return 1 - math.exp(-redundancy) # Compute zSym (symmetrized Atkinson inequality indicator) def plato2atkinson(a): return 1 - ((1 - a) / (1 + a)) ** a # zPlato: Convert zSym to zPlato using the Newton-Raphson iteration.def atkinson2plato(z_sym) def deriv(a): d = (1 - a) / (1 + a) return -d ** a * (math.log(d) - 2 * a / (1 - a ** 2)) def func(a, b): return plato2atkinson(a) - b def newton_raphson(a, b, iter, tol): if iter >= 100 or abs(func(a, b)) < tol: return a, iter else: return newton_raphson(a - func(a, b) / deriv(a), b, iter + 1, tol) if z_sym >= 0.99999999999999: return 1, 0 elif z_sym <= 0: return 0, 0 elif z_sym < 0.001: return math.sqrt(z_sym * 0.5), 0 else: initial_guess = 0.18992 + 0.72791 * z_sym return newton_raphson(initial_guess, z_sym, 0, 1e-12) # -- Usage example: def main(): data_points = [(50, 2.5), (40, 47.5), (9, 27), (1, 23)] r_sym = compute_theil_redundancy(data_points) z_sym = theil2atkinson(r_sym) z_plato, steps = atkinson2plato(z_sym) print(f"rSym: {r_sym}") print(f"zSym: {z_sym}") print(f"zPlato: {z_plato}") print(f"Newton-Raphson iterations: {steps}") if __name__ == "__main__": main() # rSym: 1.161710269336159 # zSym: 0.6870495067042661 # zPlato: 0.6880377297113732 # Newton-Raphson iterations: 3

-- Example in Haskell for how to compute the Plato inequality indicator -- Goetz Kluge, 2025-06-25 -- Compute rSym (symmetrized Theil redundancy) from a table of pairs (a,b). type PairsTable = [(Double,Double)] type RSym = Double computeTheilRedundancy :: PairsTable -> RSym computeTheilRedundancy pairs = 0.5 * sum [log (a / b) * ((a / aTotal) - (b / bTotal)) | (a, b) <- pairs] where aTotal = sum [a | (a, _) <- pairs] bTotal = sum [b | (_, b) <- pairs] -- Compute zSym (symmetrized Atkinson inequality indicator) theil2Atkinson :: Double -> Double theil2Atkinson redundancy = 1 - exp (-redundancy) -- zPlato: Convert zSym to zPlato using the Newton-Raphson iteration. atkinson2Plato :: Double -> (Double, Int) atkinson2Plato zSym | zSym >= 0.99999999999999 = (1,0) | zSym <= 0 = (0,0) | zSym < 0.001 = (sqrt (zSym * 0.5), 0) | otherwise = let initialGuess = 0.18992 + 0.72791 * zSym in newtonRaphson initialGuess zSym 0 1e-12 newtonRaphson :: Double -> Double -> Int -> Double -> (Double, Int) newtonRaphson a b iter tol | iter >= 100 || abs (func a b) < tol = (a, iter) | otherwise = newtonRaphson (a - func a b / deriv a) b (iter + 1) tol deriv :: Double -> Double deriv a = let d = (1 - a) / (1 + a) in -d ** a * (log d - 2 * a / (1 - a ** 2)) func :: Double -> Double -> Double func a b = plato2atkinson a - b plato2atkinson :: Double -> Double plato2atkinson a = 1 - ((1 - a) / (1 + a)) ** a -- Usage example: main :: IO () main = do let dataPoints = [(50,2.5),(40,47.5),(9,27),(1,23)] let rSym = computeTheilRedundancy dataPoints let zSym = theil2Atkinson rSym let (zPlato, steps) = atkinson2Plato zSym putStrLn $ "rSym: " ++ show rSym putStrLn $ "zSym: " ++ show zSym putStrLn $ "zPlato: " ++ show zPlato putStrLn $ "Newton-Raphson iterations: " ++ show steps

Alternative to: #Gini #GiniIndex #GiniCoefficient

The basic operations to compute the Platon inequality indicator from a set of data pairs now are explained not only in Haskell, but also in Python.

web.archive.org/web/20250625...

#inequality #Theil #Atkinson #Plato #Platoinequality #Hoover

symmetrized Theil|symmetrized Atkinson|Plato|Gini|Hoover|inequality acceptance 0,4190|34,23 %|44,17 %|41,99 %|29,66 %|-0,1224 1,2177|70,41 %|70,08 %|59,90 %|45,72 %|-0,7605 2,0736|87,43 %|84,27 %|70,24 %|57,64 %|-1,4972 2,9617|94,83 %|92,25 %|76,84 %|65,90 %|-2,3028 3,8554|97,88 %|96,40 %|80,92 %|70,73 %|-3,1480 4,7437|99,13 %|98,40 %|83,45 %|73,42 %|-4,0095 5,6244|99,64 %|99,31 %|85,06 %|75,51 %|-4,8693 6,4982|99,85 %|99,70 %|86,11 %|78,84 %|-5,7098 7,3664|99,94 %|99,87 %|86,83 %|81,31 %|-6,5534 8,2303|99,97 %|99,95 %|87,33 %|83,16 %|-7,3987 9,0905|99,99 %|99,98 %|87,69 %|84,54 %|-8,2451 9,9478|100,00 %|99,99 %|87,95 %|85,57 %|-9,0921 10,8028|100,00 %|100,00 %|88,14 %|86,35 %|-9,9392 11,6557|100,00 %|100,00 %|88,28 %|86,94 %|-10,7863 12,5070|100,00 %|100,00 %|88,39 %|87,38 %|-11,6332

The Plato inequality index is an entropy measure. For data sets which yield Gini indices between 20% and 60%, the Plato is quite similar to the Gini. But the Plato detects extreme inequalities much better.

Test data and tools: drive.proton.me/urls/QGQ8V63...

#Gini #GiniIndex #GiniCiefficient

Amartya Sen was not happy with Theil's measure being called an "entropy". From Amartya Sen's "On Economic inequity" I learned a lot about inequity measures. But entropy seems not do go down too well with him (1973) and his co-author James E. Foster (1997). When describing the "interesting" "Theil entropy" (chapter 2.11), Sen sees a contradiction between entropy being a measure of "disorder" in thermodynamics and entropy being a measure for "equality". If you assume that equality is "order" and thus an antonym for "disorder", then you may believe - Sen even calls it a "fact" - that the Theil coefficient is computed from an "arbitrary formula". However, there is no contradiction: The Theil measure is a redundancy (the gap between the entropy of something and the maximum entropy which it can take; see also ISO/IEC 2382-16). That is the answer to Sen's objection. High equality leads to a low redundancy and high entropy, whereas high inequity leads to a low entropy and high redundancy. The higher the redundancy, the more needs to be redistributed (re-ordered) to obtain an perfectly even distribution. Götz W. Kluge, 2009

Sorry, @pedrohalbuquerque.net, I accidentally deleted this post. Luckily I kept the source for the image and the ALT-text.

#Gini, #GiniIndex, #TheilRedundancy

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

📈 Uzbekistan’s Gini index reached 34.6% in 2024 (up from 32.9% in 2021). Inequality grew post-COVID, increasing from 32.9% in 2021 to 34.5% in 2023. However, the growth of inequality slowed down in 2024.

#Uzbekistan #GiniIndex #Inequality

🔗Visit @ihri_uzb on Telegram for more.

Die Veränderung des #GiniIndex für die Einkommens- und Vermögensverteilung über viele Jahre hinweg zu berechnen, ist nicht einfach. Vor langer Zeit hatte ich mal damit herumgspielt un d bid aus dem Thema raus. Mit welchen Daten arbeiten wir heute? bsky.app/profile/wahl...

Unbedingt! #Taxtherich #Taxmenow #GiniIndex

Wurde Deutschland vor Kurzem nicht auch aufgefordert, den Wohlstand gerechter zu verteilen, da die Schere zwischen Arm und Reich immer weiter auseinanderklafft? #GiniIndex