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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 | Source: | 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. | Keywords: | Size-frequency distribution; Rank-frequency distribution; Shape | Document URI: | http://hdl.handle.net/1942/11518 | ISSN: | 0306-4573 | e-ISSN: | 1873-5371 | DOI: | 10.1016/j.ipm.2010.03.009 | ISI #: | 000288407300008 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2012 |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Relations 1.pdf Restricted Access | Published version | 401.61 kB | Adobe PDF | View/Open Request a copy |
Relations 2.pdf | Peer-reviewed author version | 511.35 kB | Adobe PDF | View/Open |
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