The distribution of the uncitedness factor and its functional relation with the impact factor

Abstract

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.