Lotka's Bibliometric Inverse-Power Law: Calibrating the Model and Exploring a Common Conceptual Error

Abstract: Two forms of Lotka’s Law appear in the literature. The first, which is the traditional form, holds that the number of authors who publish exactly N first-author papers in primary, technical journals is proportional to 1/N2. The second holds that the number of authors who publish at least N first-author papers is proportional to 1/N, based on pseudo-integration of the first. We show that the two forms are not equivalent, despite assertions claiming that they are. We also show that the median contribution of authors who publish in primary journals is one paper, but that the theoretical average number of papers-per-author is undefined.