Medeiros (2006) defined an average affluence gap. Weighted gap (with weights \(w_1,w_2,...,w_n\)) is given by:
$$R^{Me}= \frac{\sum_{i=1}^n \max\{x_i-\rho_w,0\}w_i}{\sum_{i=1}^nw_i},$$
where \(x_i\) is an income of individual \(i\), \(n\) is the number of individuals, \(\rho_w\) is the richness line.
Medeiros' index is not standarized and is an absolute measure of richness.