Hoover index

The Hoover index, also known as the Robin Hood index or the Schutz index, is a measure of income metrics. It is equal to the portion of the total community income that would have to be redistributed (taken from the richer half of the population and given to the poorer half) for there to be income uniformity.
It can be graphically represented as the longest vertical distance between the Lorenz curve, or the cumulative portion of the total income held below a certain income percentile, and the 45 degree line representing perfect equality. 
The Hoover index is typically used in applications related to socio-economic class (SES) and health. It is conceptually one of the simplest inequality indices used in econometrics. A better known inequality measure is the Gini coefficient which is also based on the Lorenz curve.
Computation.
Let formula_1 be the income of the formula_2-th person and formula_3 be the mean income. Then the Hoover index formula_4 is:
formula_5
This value can also be computed using quantiles. For the formula, a notation is used, where the amount formula_6 of quantiles only appears as upper border of summations. Thus, inequities can be computed for quantiles with different widths formula_7. For example, formula_8 could be the income in the quantile #i and formula_9 could be the amount (absolute or relative) of earners in the quantile #i. formula_10 then would be the sum of incomes of all formula_6 quantiles and formula_12 would be the sum of the income earners in all formula_6 quantiles.
Computation of the Robin Hood index formula_4:
H = {\frac{1}{2}} \sum_{i=1}^N \left| {\frac (Describes about 50 different inequality measures.)