What are the limitations of the IHDI?
The IHDI captures the inequality in distribution of the HDI dimensions. However, it is not association sensitive, meaning that it does not account for overlapping inequalities—whether the same people are at the lower end of each distribution. Also, individual values of education and income can be zero or even negative (for income), so they have been adjusted to non-negative non-zero values uniformly across countries. This adjustment can reshape the distributions a bit, so it is fair to say that the Atkinson inequality measure provides an approximation of the magnitude of inequality.