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The OECD created a bar chart that compares the number of generations necessary for low-income families to get the average income in countries part of the OECD. [28] As in the classical interpretation of the Great Gatsby Curve, the lowest inequality can be seen in Nordic countries, and it only takes about two to three generations.
Users of the R data analysis software can install the "ineq" package which allows for computation of a variety of inequality indices including Gini, Atkinson, Theil. A MATLAB Inequality Package Archived 2008-10-04 at the Wayback Machine, including code for computing Gini, Atkinson, Theil indexes and for plotting the Lorenz Curve. Many examples ...
The Atkinson index is defined as: (, …,) = {(=) / (=) / = (,...,) = +where is individual income (i = 1, 2, ..., N) and is the mean income.. In other words, the Atkinson index is the complement to 1 of the ratio of the Hölder generalized mean of exponent 1−ε to the arithmetic mean of the incomes (where as usual the generalized mean of exponent 0 is interpreted as the geometric mean).
In the discrete case, an economic inequality index may be represented by a function I(x), where x is a set of n economic values (e.g. wealth or income) x={x 1,x 2,...,x n} with x i being the economic value associated with "economic agent" i.
Income inequality has fluctuated considerably since measurements began around 1915, declining between peaks in the 1920s and 2007 (CBO data [2]) or 2012 (Piketty, Saez, Zucman data [15]). Inequality steadily increased from around 1979 to 2007, with a small reduction through 2016, [2] [16] [17] followed by an increase from 2016 to 2018. [18]
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The two world wars were very big factors in keeping inequality low at the time. The rich were being heavily taxed by governments to finance the two conflicts, lowering inequality. After the wars, more socialist movements and trade unions emerged demanding better pay and working conditions, giving workers more power and lowering inequality.
Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount Bhatia–Davis inequality , an upper bound on the variance of any bounded probability distribution