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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/11518

Title: Relations between the shape of a size-frequency distribution and the shape of a rank-frequency distribution
Authors: EGGHE, Leo
Waltman, Ludo
Issue Date: 2011
Publisher: Elsevier
Citation: INFORMATION PROCESSING & MANAGEMENT, 47(2). p. 238-245
Abstract: We study the dependence of the shape of the rank-frequency distribution g on the shape of the size-frequency distribution f and vice versa. We show mathematically that g is convexly decreasing if and only if f is monotonically decreasing and that g has an S-shape (i.e., g is first convexly decreasing and then concavely decreasing) if and only if f is first increasing and then decreasing. To illustrate our mathematical results, we empirically analyze size- and rank-frequency distributions of the number of articles and of the impact factor of journals in various scientific fields. We find that most of the size-frequency distributions that we examine are first increasing and then decreasing. Most of the rank-frequency distributions that we examine have an S-shape. However, the concave part of the S-shape is sometimes very small.
URI: http://hdl.handle.net/1942/11518
DOI: 10.1016/j.ipm.2010.03.009
ISI #: 000288407300008
ISSN: 0306-4573
Category: A1
Type: Journal Contribution
Validation: ecoom, 2012
Appears in Collections: Research publications

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