Is there any social inequality measure for categorical or ordinal variables, based on a goodness of fit
chi squared test (distance from an uniform distribution)?
Example: part of my data is unemployment rates by 4 age groups. I know that inequality is minimum if the rates are equal for the 4 age groups (uniform distribution), for example [0.04, 0.04, 0.04, 0.04].
N.B. The sum of these rates is $\neq$ 1.