wINEQ (version 1.2.1)

AN_Y: Abul Naga and Yalcin index

Description

Computes Abul Naga and Yalcin inequality measure of a given variable taking into account weights.

Usage

AN_Y(X, W = rep(1, length(X)), a = 1, b = 1)

Value

The value of Abul Naga and Yalcin 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 positive parameter. See more in details

Details

Let \(m\) be the median category, \(n\) be the number of categories and \(P_{i}\) be the cumulative distribution of \(i\)-th category. The following index with respect to the parameters a and b was proposed by Abul Naga and Yalcin (2008): $$I=\frac{a\sum_{i<m}^{n}P_{i}-b\sum_{i\geq m}^{n}P_{i}+b(n+1-m)}{0.5(a(m-1)+b(n-m))}$$

References

Ramses H. Abul Naga and Tarik Yalcin: (2008) Inequality Measurement for ordered response health data, Journal of Health Economics 27(6);

Examples

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

data(Well_being)
# Abul Naga and Yalcin index for health assessment with sample weights
X=Well_being$V1
W=Well_being$Weight
AN_Y(X,W)