Hierarchical distributions and Bradford's Law

Abstract

A probabilistic model of random fragmentation of the unit line provides the formal underpinning for deriving a distribution of the articles published in any field, over journals ranked in decreasing order of productivity. No assumptions need to be made about the causal mechanism that brings about such a distribution. Interestingly, the proportion of articles, p, that may be obtained from some given proportion, q, of the most productive journals, is found to be greater than q by a factor -q In q. This may be interpreted as the additional “information” retrieved over the unranked case, and is a direct consequence of the procedure of ranking the journals. While the distribution obtained reproduces the general shape of a cumulative frequency log-rank graph of publications data, to ensure good fit to data, a parameter has to be introduced. This parameter may be considered to incorporate the effects of possible deviation from randomness, and is suggested as an indirect measure of concentration. © 1992 John Wiley & Sons, Inc.

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