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Title: | Study of the rank- and size-frequency functions in case of power law growth of sources and items and proof of Heaps' law | Authors: | EGGHE, Leo | Issue Date: | 2013 | Source: | INFORMATION PROCESSING & MANAGEMENT, 49(1), p. 99-107. | Abstract: | Supposing that the number of sources and the number of items in sources grow in time according to power laws, we present explicit formulae for the size- and rank-frequency functions in such systems. Size-frequency functions can decrease or increase while rank-frequency functions only decrease. The latter can be convex, concave, S-shaped (first convex, then concave) or reverse S-shaped (first concave, then convex). We also prove that, in such systems, Heaps’ law on the relation between the number of sources and items is valid. | Keywords: | Power law growth; Rank-frequency function; Size-frequency function; Heaps’ law | Document URI: | http://hdl.handle.net/1942/13127 | ISSN: | 0306-4573 | e-ISSN: | 1873-5371 | DOI: | 10.1016/j.ipm.2012.02.004 | ISI #: | 000313466600007 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2014 |
Appears in Collections: | Research publications |
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File | Description | Size | Format | |
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study 1.pdf Restricted Access | 223.48 kB | Adobe PDF | View/Open Request a copy | |
study 2.pdf | Peer-reviewed author version | 361.49 kB | Adobe PDF | View/Open |
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