Atkinson {wINEQ}

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)

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.

Value

The value of Atkinson coefficient.

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)