Generalized entropy index

The generalized entropy index has been proposed as a measure of income inequality in a population.

[1] 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 addition, interpretation of biodiversity as entropy has also been proposed leading to uses of generalized entropy to quantify biodiversity.

[2] The formula for general entropy for real values of

where N is the number of cases (e.g., households or families),

is the income for case i and

is a parameter which regulates the weight given to distances between incomes at different parts of the income distribution.

the index is especially sensitive to the existence of large incomes, whereas for small

the index is especially sensitive to the existence of small incomes.

The GE index satisfies the following properties: An Atkinson index for any inequality aversion parameter can be derived from a generalized entropy index under the restriction that

ϵ = 1 − α

- i.e. an Atkinson index with high inequality aversion is derived from a GE index with small

The formula for deriving an Atkinson index with inequality aversion parameter

ϵ = 1 − α

Note that the generalized entropy index has several income inequality metrics as special cases.

For example, GE(0) is the mean log deviation a.k.a.

Theil L index, GE(1) is the Theil T index, and GE(2) is half the squared coefficient of variation.