- Mathematical Formulations of Bradford's Law; a Discussion of its Historical Development
- No.24, p.11-29
In this paper, the author reviews the diverse studies on mathematical formulations of Bradford’s law, which is a representative distribution law in bibliometrics.
Since S. C. Bradford presented the law in 1934, there have been three trends of the study. In the first trend, researchers tried to formulate a law following the proportional expression originally shown by Bradford. The studies of Vickery, Leimkuhler, Wilkinson, and others are classified in this trend. In the second trend, researchers tried to lead a formula according to the shape of graphs describing observed values. The studies of Brookes, Haspers, Asai, and others are classified in this trend. And in the third trend, researchers have attempted to produce a formula from various probabilistic models. The author shows Simon’s model, Onodera’s model, and Naranan’s model as sophisticated mathematical models.
These formulations are so diverse that there is still no formula which can be recognized as a universal one. The author concludes that to test the fitness of each formula with observed data stastistically and to establish the most desirable formulation of Bradford’s law are urgent tasks in bibliometric studies.
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