Generalized entropy index
||This article provides insufficient context for those unfamiliar with the subject. (December 2010)|
The generalized entropy index is a general formula for measuring redundancy in data. The redundancy can be viewed as inequality, lack of diversity, non-randomness, compressibility, or segregation in the data. The primary use is for income inequality. It is equal to the definition of redundancy in information theory that is based on Shannon entropy when α = 1 which is also called the Theil index (TT) in income inequality research. Completely "diverse" data has no redundancy so that GE=0, so that it increases in the opposite direction of a Diversity index. It increases with order rather than disorder, so it is a negated measure of entropy.
The formula is
where is the income for individual i that is part of N and is the weight given to distances between incomes at different parts of the income distribution. Sometimes a different notation is used where = ß + 1.
For lower values of close to 0, GE is more sensitive to changes in the lower incomes and vice versa for values closer to 1. Theil's TT has and the negative of the mean log deviation has . When the value is half the square of the coefficient of variation:
The generalized entropy index is a transformation of the Atkinson index where . The transformation is [verification needed (see talk page)], so that the Atkinson index is a probability instead of entropy.
When the of is replaced with (for example, income/person becomes persons/income) then is equivalent to .
- Theil index
- Atkinson index
- Lorenz curve
- Gini coefficient
- Hoover index (a.k.a. Robin Hood index)
- Suits index
- Income inequality metrics
- Rényi entropy
|This article needs additional citations for verification. (November 2010)|