The uncitedness factor of a journal is its fraction of uncited articles. Given a set of journals (e.g. in a field) we can
determine the rank-order distribution of these uncitedness factors. Hereby we use the Central Limit Theorem which is valid
for uncitedness factors since it are fractions, hence averages. A similar result was proved earlier for the impact factors
of a set of journals. Here we combine the two rank-order distributions, hereby eliminating the rank, yielding the functional
relation between the impact factor and the uncitedness factor. It is proved that the decreasing relation has an S-shape: first
convex, then concave and that the inflection point is in the point (μ′, μ) where μ is the average of the impact factors and
μ′ is the average of the uncitedness factors.
In this study an attempt is made to establish new bibliometric indicators for the assessment of research in the Humanities.
Data from a Dutch Faculty of Humanities was used to provide the investigation a sound empirical basis. For several reasons
(particularly related to coverage) the standard citation indicators, developed for the sciences, are unsatisfactory. Target
expanded citation analysis and the use of oeuvre (lifetime) citation data, as well as the addition of library holdings and
productivity indicators enable a more representative and fair assessment. Given the skew distribution of population data,
individual rankings can best be determined based on log transformed data. For group rankings this is less urgent because of
the central limit theorem. Lifetime citation data is corrected for professional age by means of exponential regression.
CHATTERJI, S. D., A principle of subsequences in probability theory: The centrallimittheorem, Adv. Math. 13 (1974), 31-54; correction, ibid. 14 (1974), 266-269. MR 49 #6312
A principle of subsequences in probability theory