Distributions for cited articles from individual subjects and years

TL;DR

This study compares different statistical distributions to model citation counts for academic articles within specific subjects and years, finding that the hooked power law and lognormal distributions are most suitable but have limitations.

Contribution

It evaluates the fit of power law, lognormal, and hooked power law distributions to citation data across multiple disciplines, highlighting the limitations of power law models.

Findings

Power law is unsuitable for citation data from single subjects and years.

Hooked power law and lognormal distributions fit best for some categories.

Parameter estimates for these models are often unreliable.

Abstract

The citations to a set of academic articles are typically unevenly shared, with many articles attracting few citations and few attracting many. It is important to know more precisely how citations are distributed in order to help statistical analyses of citations, especially for sets of articles from a single discipline and a small range of years, as normally used for research evaluation. This article fits discrete versions of the power law, the lognormal distribution and the hooked power law to 20 different Scopus categories, using citations to articles published in 2004 and ignoring uncited articles. The results show that, despite its popularity, the power law is not a suitable model for collections of articles from a single subject and year, even for the purpose of estimating the slope of the tail of the citation data. Both the hooked power law and the lognormal distributions fit best for some subjects but neither is a universal optimal choice and parameter estimates for both seem to be unreliable. Hence only the hooked power law and discrete lognormal distributions should be considered for subject-and-year-based citation analysis in future and parameter estimates should always be interpreted cautiously.