An exact calculation of Price's law for the law of Lotka |
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Authors: | L Egghe |
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Affiliation: | (1) Present address: LUC, Universitaire Campus, B-3610 Diepenbeek, Belgium;(2) UIA, Universiteitsplein 1, B-2610 Wilrijk, Belgium |
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Abstract: | Price's law asserts — in its simpliest version — that
authors produce half of the papers made by the total ofN authors. More generally: the topN
(0< <1) authors produce a fraction (0< <1) of the papers made by the total ofN authors and the Price's law says that ![theta](/content/t0722n319573k338/xxlarge952.gif) ![ap](/content/t0722n319573k338/xxlarge8776.gif) . In this paper — using Lotka's law — we prove a mathematical relationship of in function of and the parameter (the mean number of papers per author) and investigate when ![theta](/content/t0722n319573k338/xxlarge952.gif) ![ap](/content/t0722n319573k338/xxlarge8776.gif) . 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). |
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