Title
Relations between the shape of a size-frequency distribution and the shape of a rank-frequency distributionRelations between the shape of a size-frequency distribution and the shape of a rank-frequency distribution
Author
Faculty/Department
Faculty of Social Sciences. Instructional and Educational Sciences
Research group
Book, Library and Information
Publication type
article
Publication
Oxford,
Subject
Documentation and information
Source (journal)
Information processing and management. - Oxford
Volume/pages
47(2011):2, p. 238-245
ISSN
0306-4573
ISI
000288407300008
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
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.
E-info
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