Elements of concentration theory

Abstract

We review some concentration measures proposed in the literature and present a set of principles that good concentration measures must fulfill . We moreover look into some of the consequences of these principles. The transfer principle is extended to yield a new family of principles, denoted E(p), but a concentration measure can only satisfy E(p) for at most one p. We discuss briefly the issue of sensitivity to transfers and show that Heine's dispersion measures are related to some well-known concentration measures.