wINEQ (version 1.2.1)

AF: Allison and Foster index

Description

Computes Allison and Foster inequality measure of a given variable taking into account weights.

Usage

AF(X, W = rep(1, length(X)), norm = TRUE)

Value

The value of Allison and Foster coefficient.

Arguments

X

is a data vector (numeric or ordered factor)

W

is a vector of weights

norm

(logical). If TRUE (default) then index is divided by a maximum possible value which is a difference between maximum and minimum of X

Details

Let \(c=(c_{1},...,c_{n})\) be the vector of categories in increasing order, \(m\) be the median category and \(p_i\) be a share of \(i\)-th category. The following index was proposed by Allison and Foster (2004): $$AF = \frac{\sum_{i=m}^n c_{i} p_{i} }{\sum_{i=m}^n p_{i}} - \frac{\sum_{i=1}^{m-1} c_{i} p_{i}}{\sum_{i=1}^{m-1} p_{i}}$$ Note that above formula is valid only for numerical values. Thus, in order to compute AF for ordered factor, X is converted to numerical variable.

References

Allison R. A., Foster J E.: (2004) Measuring health inequality using qualitative data, Journal of Health Economics

Examples

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

data(Well_being)
# Allison and Foster index for health assessment with sample weights
X=Well_being$V11
W=Well_being$Weight
AF(X,W)