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Slovenia's Current Research Information System (SICRIS) currently hosts86,443 publications with citation data from 8,359 researchers working on thewhole plethora of social and natural sciences from 1970 till present. Usingthese data, we show that the citation distributions derived from individualpublications 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 theinstitution and field of research. Distributions of indexes that quantify thesuccess 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 andHirsch'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 ofresearchers. In special cases, particularly for institutions with a stronglyhierarchical constitution and research fields with high self-citation rates,exponential distributions can be observed as well. Both indexes yielddistributions with equivalent statistical properties, which is a strongindicator for their consistency and logical connectedness. At the same time,differences in the assessment of citation histories of individual researchersstrengthen their importance for properly evaluating the quality and impact ofscientific output.

journal of informetrics

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