The generalized entropy index has been proposed as a measure of income inequality in a population. It is derived from information theory as a measure of redundancy in data. In information theory a measure of redundancy can be interpreted as non-randomness or data compression; thus this interpretation also applies to this index. In additional interpretation of the index is as biodiversity as entropy has also been proposed as a measure of diversity.
Formula
The formula for general entropy for real values of
where N is the number of cases (e.g., households or families),
A feature of the generalized entropy index is that it can be transformed into a subclass of the Atkinson index with
Note that the generalized entropy index has several income inequality metrics as special cases. For example, GE(0) is the mean log deviation, GE(1) is the Theil index, and GE(2) is half the squared coefficient of variation.