Generalized entropy index

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.

The formula for general entropy for real values of ${\displaystyle \alpha }$ is:

where N is the number of cases (e.g., households or families), ${\displaystyle y_{i}}$ is the income for case i and ${\displaystyle \alpha }$ is the weight given to distances between incomes at different parts of the income distribution.

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