Abstract: It is well known that the h-index has been originally introduced by analyzing a simple deterministic model of individual’s scientific activity. The basic features of Hirsch’s model are listed as follows: i) constant publication rate in time; ii) constant number of citations gained by each paper per unit time. One of its predictions is the formation of (approximately) linear negative slope citation-paper rank distribution. However, the actual citation-paper rank distributions obtained by analyzing real life scientometric data are, apart from some rare exceptions, convex and far from linear. In this paper we consider two possible reasons that might explain the deviation from linear negative-slope (Hirsch) citation-paper rank distribution. The first one is an increasing in time publication rate, reflecting the fact of growing productivity in the course of a scientific career, as well as the increase of publication rates on global scale. The second one is an increasing in time number of citations gained by individual papers per unit time, associated, e.g. with improving publication quality or growing popularity. Both factors lead to a shaping of convex citation-paper rank distribution from the linear one, in a way that generalizes Hirsch’s results.

Keywords: citation-paper rank distributions, Hirsch’s model, linear negative-slope distribution, convex distributions, time dependence, empirical relationships, scientometric data analysis

ACM Classification Keywords: H. Information Systems, H.2. Database Management, H.2.8. Database applications, subject: Scientific databases; I. Computing methodologies, I.6 Simulation and Modeling, I.6.4. Model Validation and Analysis

Link:

SHAPING THE CITATION-PAPER RANK DISTRIBUTIONS: BEYOND HIRSCH’S MODEL

Vladimir Atanassov, Ekaterina Detcheva

http://www.foibg.com/ijima/vol03/ijima03-01-p06.pdf