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Title
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Relations between the shape of a size-frequency distribution and the shape of a rank-frequency distribution
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Author
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Abstract
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| 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. |
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Language
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English
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Source (journal)
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Information processing and management. - Oxford
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Publication
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Oxford
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2011
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ISSN
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0306-4573
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DOI
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10.1016/J.IPM.2010.03.009
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Volume/pages
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47
:2
(2011)
, p. 238-245
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ISI
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000288407300008
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Full text (Publisher's DOI)
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Full text (publisher's version - intranet only)
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