Zipf's law and log-normal distributions in measures of scientific output across fields and institutions: 40 years of Slovenia's research as an example

Abstract

Slovenia's Current Research Information System (SICRIS) currently hosts 86,443 publications with citation data from 8,359 researchers working on the whole plethora of social and natural sciences from 1970 till present. Using these data, we show that the citation distributions derived from individual publications have Zipfian properties in that they can be fitted by a power law $P(x)\sim x^{-\alpha }$, with $\alpha$ between 2.4 and 3.1 depending on the institution and field of research. Distributions of indexes that quantify the success of researchers rather than individual publications, on the other hand, cannot be associated with a power law. We find that for Egghe's g-index and Hirsch's h-index the log-normal form $P(x)\sim \exp [-a\ln x-b(\ln x{)}^2]$ applies best, with $a$ and $b$ depending moderately on the underlying set of researchers. In special cases, particularly for institutions with a strongly hierarchical constitution and research fields with high self-citation rates, exponential distributions can be observed as well. Both indexes yield distributions with equivalent statistical properties, which is a strong indicator for their consistency and logical connectedness. At the same time, differences in the assessment of citation histories of individual researchers strengthen their importance for properly evaluating the quality and impact of scientific output.

arXiv comment8 pages, 3 figures; accepted for publication in Journal of Informetrics [supplementary material available at http://www.matjazperc.com/sicris/stats.html]

References in corpus (20)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• An index to quantify an individual's scientific research output
• Power-law distributions in empirical data
• Power laws, Pareto distributions and Zipf's law
• The structure of scientific collaboration networks
• How Popular is Your Paper? An Empirical Study of the Citation Distribution
• Structure of Growing Networks: Exact Solution of the Barabasi--Albert's Model
• Connectivity of Growing Random Networks
• Does the h-index have predictive power?
• Organization of Growing Random Networks
• Universality of citation distributions: towards an objective measure of scientific impact
• Stretched exponential distributions in Nature and Economy: ``Fat tails'' with characteristic scales
• Citation Statistics from 110 Years of Physical Review
• On the Frequency of Severe Terrorist Events
• Degree Distributions of Growing Networks
• Scaling Behaviour of Developing and Decaying Networks
• The first-mover advantage in scientific publication
• The influence of self-citation corrections on Egghe's g index

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