On A Class of Human Development Index Measures - Srijit Mishra and Hippu Salk Kristle Nathan

If we refer to this as the local ideal position then the locus of all such positions is the line of equality, which can be obtained by joining the origin and the ideal in the n-dimensional space. [...] An Empirical Example We make use of indicator values with regard to the dimensions of education, health and income to compute HDIα (α=1,2,3), respective ranks, Rα, across 177 countries, change in ranks, and for higher order HDIs the deviation from the line of equality, NorPα, and the deviation from the ideal path, NorQα. [...] Appendix 1: Two Other Measures of Position Penalty A second measure of position penalty is to take the deviation from the line of equality as a proportion of the maximum possible deviation for that mean, μ. [...] I A'k' x2 k O Ax k'' 1 Figure 4: Deviation from the line of equality 9 A third measure is to take the deviation from the line of equality as a proportion of the maximum possible deviation. [...] Appendix 2: A Second Measure of Path Penalty A second measure of path penalty captures the deviation by calculating the distance between the new position and a corresponding position in the ideal path, Dll’ (see Figure 3).