wINEQ (version 1.2.1)

Atkinson: Atkinson index

Description

Computes Atkinson inequality measure of a given variable taking into account weights.

Usage

Atkinson(X, W = rep(1, length(X)), e = 1)

Value

The value of Atkinson coefficient.

Arguments

X

is a data vector

W

is a vector of weights

e

is a coefficient of aversion to inequality, by default 1

Details

Atkinson coefficient with respect to parameter \(\epsilon\) is given by $$1-\frac{1}{\mu}{(\frac{1}{n}\sum_{i=1}^{n} x_{i}^{1-\epsilon} )}^{\frac{1}{1-\epsilon}}$$ for \(\epsilon \neq 1\) and $$1-\frac{1}{\mu}{(\prod_{i=1}^{n} x_i)}^{\frac{1}{n}}$$ for \(\epsilon=1\).

References

Atkinson A. B.: (1970) On the measurement of inequality, Journal of Economic Theory

Examples

# Compare weighted and unweighted result
X=1:10
W=1:10
Atkinson(X)
Atkinson(X,W)

data(Tourism)
# Atkinson index for Total expenditure with sample weights
X=Tourism$Total_expenditure
W=Tourism$Sample_weight
Atkinson(X,W)