  We provide a survey of the Kolkata index of social inequality, focusing in
particular on income inequality. Based on the observation that inequality
functions (such as the Lorenz function), giving the measures of income or
wealth against that of the population, to be generally nonlinear, we show that
the fixed point (like Kolkata index k) of such a nonlinear function (or
related, like the complementary Lorenz function) offer better measure of
inequality than the average quantities (like Gini index). Indeed the Kolkata
index can be viewed as a generalized Hirsch index for a normalized inequality
function and gives the fraction k of the total wealth possessed by the rich
(1-k) fraction of the population. We analyze the structures of the inequality
indices for both continuous and discrete income distributions. We also compare
the Kolkata index to some other measures like the Gini coefficient and the
Pietra index. Lastly, we provide some empirical studies which illustrate the
differences between the Kolkata index and the Gini coefficient.
