G G Naumis and G Cocho 2007 New J. Phys. 9 286 doi:10.1088/1367-2630/9/8/286
The tails of rank-size distributions due to multiplicative processes: from power laws to stretched exponentials and beta-like functions
G G Naumis and G Cocho
Show affiliationsAlthough power laws have been used to fit rank distributions in many different contexts, they usually fail at the tail. Here we show that many different data in rank laws, like in granular materials, codons, author impact in scientific journals, etc are very well fitted by a β-like function ({a, b} distribution). Since this distribution is indeed ubiquitous, it is reasonable to associate it with some kind of general mechanism. In particular, we have found that the macrostates of the product of discrete probability distributions imply stretched exponential-like frequency-rank functions, which qualitatively and quantitatively can be fitted with the {a,b} distribution in the limit of many random variables. We show this by transforming the problem into an algebraic one: finding the rank of successive products of a given set of numbers.
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Issue 8 (August 2007)
Received 17 May 2007
Published 28 August 2007
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The tails of rank-size distributions due to multiplicative processes: from power laws to stretched exponentials and beta-like functions
G G Naumis and G Cocho 2007 New J. Phys. 9 286
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