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It is conceptually one of the simplest inequality indices used in econometrics. A more frequently encountered inequality measure is the Gini coefficient which is based on the summation, over all income-ordered population-percentiles, of the cumulative income up to each percentile. That sum is divided by the maximum value that it could have (its ...
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).
Keeping these points in mind helps to understand the problems caused by the improper use of inequality measures. However, they do not render inequality coefficients invalid. If inequality measures are computed in a well explained and consistent way, they can provide a good tool for quantitative comparisons of inequalities.
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
The inverse x(F) may not exist because the cumulative distribution function has intervals of constant values. However, the previous formula can still apply by generalizing the definition of x(F): = {: ()} where inf is the infimum. For an example of a Lorenz curve, see Pareto distribution.
For example, taking the world economy as a whole and income distribution for all human beings, different scholars estimate the global Gini index to range between 0.61 and 0.68. [11] [12] As with other inequality coefficients, the Gini coefficient is influenced by the granularity of the measurements. For example, five 20% quantiles (low ...
The Theil index is a statistic primarily used to measure economic inequality [1] and other economic phenomena, though it has also been used to measure racial segregation. [2] [3] The Theil index T T is the same as redundancy in information theory which is the maximum possible entropy of the data minus the observed entropy.
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.