We consider an entropic distance analog quantity based on the density of the Gini index in the Lorenz map, i.e., gintropy. Such a quantity might be used for pairwise mapping and ranking between various countries and regions based on income and wealth inequality.

Its generalization to f-gintropy, using a function of the income or wealth value, distinguishes between regional inequalities more sensitively than the original construction.

T. S. Biró, A. Telcs, M. Józsa, Z. Néda, f-Gintropy: An Entropic Distance Ranking Based on the Gini Index, Entropy (Basel) 24(3) (2022) 407