Technical Note—Exact Solution for the Bradford Distribution and Its Use in Modeling Informational Data

Philip M. Morse and Ferdinand F. Leimkuhler
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Philip M. Morse: Massachusetts Institute of Technology, Cambridge, Massachusetts
Ferdinand F. Leimkuhler: Purdue University, West Lafayette, Indiana

Operations Research, 1979, vol. 27, issue 1, 187-198

Abstract: The Bradford distribution requires a logarithmic relationship between the fraction of items having “productivity” n or more and the total, cumulative “production” of these items. An exact solution is obtained for this distribution for all integer values of n ≥ 1. The result, useful in describing library and other informational data, is compared with the Zipf and the modified geometric distributions. Examples are given of the operational value of representing informational data by one of these distributions. We develop simple tests to see how well a given sample of data conforms to one or the other distribution and apply the tests to two samples; the number of operations research articles appearing in various journals in a given time interval and the rate of use of various physics periodicals in a science library. We show that the first fits the Bradford distribution quite well, while the second fits the modified geometric distribution. We discuss some of the implications of this difference.

Date: 1979
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