A geometric model for the analysis of citation distributions

In this paper, we present an empirical study for modeling the citation distribution of papers of individual authors. We analyzed the citation records of applicants to the so called “Abilitazione Scientifica Nazionale” (ASN), a new procedure, based on scientific qualification criteria, for the recruitment of academic staff in Italy. We analyzed citation records of 131 physicists who were applicants in the ASN for a full professorship in the specific area of Condensed Matter Physics, using different mathematical models, namely: zeta, geometric, logarithmic and Pareto (of the first kind). Each model was “estimated”, on the basis of the observed citation pattern, via minimum Kullback-Leibler distance method. The geometric distribution was also considered by using a trimmed version of the estimator. As a measure of the effectiveness of the model, we computed the Kolmogorov-Smirnov distance. The most remarkable result is that the geometric distribution can provide an adequate tool for the modelization of the citation distribution of an author. Model fit may be further improved by adopting the trimming method.