Robin Hood index

The Robin Hood index, also known as the Hoover index, is a measurement of income inequality across a geographic area and is derived from the Lorenz curve.

Mathematically, the Robin Hood index for Lorenz curve $\scriptstyle L(x)$ is $\scriptstyle \max (x - L(x))$. This means that the index is derived by finding the largest vertical line, which can be drawn between a Lorenz curve for perfectly even distribution (e.g. of incomes) and the measured Lorenz curve. Theoretically the height of the rectangle surrounding the Lorenz curve is the greatest possible maximum. Therefore dividing the found line by the height of the rectangle yields a metric between 0% and 100%.

The Robin Hood Index is conceptually one of the simplest measures of inequality used in econometrics and sociology studies. 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 the society to reach financial equality.

See also

• Gini index
• Theil index
• Hoover index
• Atkinson index
• Suits index
• Generalized entropy index
• Diversity index

External links

• Bruce P Kennedy, Ichiro Kawachi, Deborah Prothrow-Stith: Income distribution and mortality: cross sectional ecological study of the Robin Hood index in the United States, BMJ 1996 (April 20th);312:1004-1007