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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/12895

Title: Study of rank- and size-frequency functions and their relations in a generalized Naranan framework
Authors: Egghe, Leo
Issue Date: 2012
Citation: MATHEMATICAL AND COMPUTER MODELLING, 55(7-8), p.1898-1903.
Abstract: 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 φ(t) and that the number of items in sources grows according to a function ψ(t). We then prove formulae for the rank-frequency function g(r) and the size-frequency function f(j) in terms of the function φ(t) and ψ(t). As a special case, we obtain Naranan’s original result that f(j) is the law of Lotka if φ and ψ 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 φ and ψ as the first system but in reverse order. Results of φ=ψ follow from this as a consequence.
URI: http://hdl.handle.net/1942/12895
Link to publication: http://www.sciencedirect.com/science/article/pii/S0895717711007321
DOI: 10.1016/j.mcm.2011.11.047
ISI #: 000300621900006
ISSN: 0895-7177
Category: A1
Type: Journal Contribution
Validation: ecoom, 2013
Appears in Collections: Research publications

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