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Research Article
Zipfian and Lotkaian continuous concentration theory
Article first published online: 21 APR 2005
DOI: 10.1002/asi.20186
Copyright © 2005 Wiley Periodicals, Inc.
Issue
Journal of the American Society for Information Science and Technology
Volume 56, Issue 9, pages 935–945, July 2005
Additional Information
How to Cite
Egghe, L. (2005), Zipfian and Lotkaian continuous concentration theory. J. Am. Soc. Inf. Sci., 56: 935–945. doi: 10.1002/asi.20186
Publication History
- Issue published online: 3 JUN 2005
- Article first published online: 21 APR 2005
- Manuscript Revised: 6 JUL 2004
- Manuscript Accepted: 6 JUL 2004
- Manuscript Received: 12 APR 2004
- Abstract
- Article
- References
- Cited By
Abstract
In this article concentration (i.e., inequality) aspects of the functions of Zipf and of Lotka are studied. Since both functions are power laws (i.e., they are mathematically the same) it suffices to develop one concentration theory for power laws and apply it twice for the different interpretations of the laws of Zipf and Lotka. After a brief repetition of the functional relationships between Zipf's law and Lotka's law, we prove that Price's law of concentration is equivalent with Zipf's law. A major part of this article is devoted to the development of continuous concentration theory, based on Lorenz curves. The Lorenz curve for power functions is calculated and, based on this, some important concentration measures such as the ones of Gini, Theil, and the variation coefficient. Using Lorenz curves, it is shown that the concentration of a power law increases with its exponent and this result is interpreted in terms of the functions of Zipf and Lotka.