Theoretical justification of the central area indices and the central interval indices

Abstract

The central area indices and the central interval indices, as introduced in Dorta-González, Scientometrics 88(3), 729-745, 2011, are studied from a theoretical point of view. They are defined in order to yield higher impact values of "selective" authors (i.e. authors with concentrated number of citations over their publications). We show that this property is not valid for every citation distribution. However,if Zipf's law is adopted for the citation distribution, we can show that the central area indices and the central interval indices have indeed higher values for more selective authors.