A basic indicator for relative contributions and a remarkable difference between a ratio of averages and an average of ratios

Abstract

This article has been inspired by the activity index and problems in its proper understanding. It studies a basic relative contribution index which is placed in the context of countries’ publication contributions. Two versions are proposed: one being an average of ratios (AoR) and the other one a ratio of averages (RoA). A Lotkaian-Zipfian framework is used to model the two versions of the proposed indicator. A remarkable difference between the two approaches (RoA vs. AoR) is found when determining the fraction of units (countries) that have a value larger than one. This observation contributes to the understanding of the differences between these two approaches.