A Generalized Index of Concentration

Abstract

A generalized nth power index of concentration is defined; for n = 1 it yields the entropy-based "relative redundancy, " and for n = 2 it yields the Ray and Singer (1973) concentration coefficient. Relations are established with a dozen other indices of concentration, diversity, fragmentation, differentiation, and inequality used in social science literature. Explicit conversion formulas are given for these often apparently unrelated indices. For multicomponent systems, equivalent two-component systems are defined.