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Title
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Study of rank- and size-frequency functions and their relations in a generalized Naranan framework
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Author
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Abstract
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| The Naranan formalism supposes that the number of sources and the number of items in sources grows exponentially. Here we extend this formalism by assuming, very generally, that the number of sources grows according to a function phi(t) and that the number of items in sources grows according to a function psi(t). We then prove formulae for the rank-frequency function g(r) and the size-frequency function f(j) in terms of the function phi(t) and psi(t). As a special case, we obtain Naranan's original result that f (j) is the law of Lotka if phi and psi are exponential functions. We also prove relations between the rank-and size-frequency functions of two systems where the second system is built on the same functions phi and psi as the first system but in reverse order. Results of phi = psi follow from this as a consequence. (C) 2011 Elsevier Ltd. All rights reserved. |
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Language
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English
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Source (journal)
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Mathematical and computer modelling. - Oxford
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Publication
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Oxford
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2012
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ISSN
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0895-7177
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DOI
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10.1016/J.MCM.2011.11.047
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Volume/pages
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55
:7-8
(2012)
, p. 1898-1903
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ISI
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000300621900006
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Full text (Publisher's DOI)
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Full text (publisher's version - intranet only)
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