A single-parameter generalization of Gini based on the 'metallic' sequences of number theory

The best-known and most-widely studied generalization of the Gini coefficient of inequality is the single-parameter extension due to authors such as David Donaldson, John Weymark, Nanak Kakwani, Shlomo Yitzhaki, and Satya Chakravarti. The ‘S-Gini' parametrization is essentially in the form of a scalar employed as an exponent on Gini's income-weight, which is the Borda rank-order. The present note considers an alternative single-parameter generalization in which income-weights are derived from Fibonacci-like sequences of numbers, each sequence being indexed by a non-negative integer. The Gini coefficient is a special case of the resulting series of indices, another of which—the ‘Fibonacci' index—is introduced, and shown to be a transfer-sensitive extension of Gini.