An exact calculation of Price's law for the law of Lotka

Abstract

Price's law asserts — in its simpliest version — that$\sqrt N$ authors produce half of the papers made by the total ofN authors. More generally: the topN ^α(0<α<1) authors produce a fraction θ (0<θ<1) of the papers made by the total ofN authors and the Price's law says that θ≈α. In this paper — using Lotka's law — we prove a mathematical relationship of θ in function of α and the parameter μ (the mean number of papers per author) and investigate when θ≈α. More-over our reasoning uses the theory of the 80/20 rule as developed in: L. EGGHE, On the 80/20-rule,Scientometrics, 10 (1986) 55–68, thereby also showing the relation betwwen the 80/20-rules (being an arithmetical form of measuring elitarism) and Price's law (being a geometric form of measuring elitarism).