wINEQ (version 1.2.1)

Apouey: Apouey index

Description

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

Usage

Apouey(
  X,
  W = rep(1, length(X)),
  a = 2/(1 - length(W[!is.na(W) & !is.na(X)])),
  b = length(W[!is.na(W) & !is.na(X)])/(length(W[!is.na(W) & !is.na(X)]) - 1)
)

Value

The value of Apouey coefficient.

Arguments

X

is a data vector (numeric or ordered factor)

W

is a vector of weights

a

is a positive parameter. See more in details

b

is a real parameter. See more in details

Details

Let \(m\) be the median category, \(n\) will be the number of categories and \(P_i\) be the cumulative distribution of \(i\)-th category. The following index was proposed by Apouey (2007): $$I = \alpha(\sum_{i\geq m}^{n}P_{i}-\sum_{i<m}^{n}P_{i}+m-\frac{n}{2}-1)+\beta$$ where \(\alpha\) and \(\beta\) are given parameters with default values \(\alpha=\frac{2}{1-n}\) and \(\beta=\frac{n}{n-1}\).

References

Apouey B.: (2007) Measuring health polarization with self-assessed health data, Health Economics 16; 875-894.

Examples

# Compare weighted and unweighted result
X=1:10
W=1:10
Apouey(X,a=2,b=2)
Apouey(X,W,a=2,b=2)

data(Well_being)
# Apouey index for health assessment with sample weights
X=Well_being$V1
W=Well_being$Weight
Apouey(X,W,a=2,b=2)