A mere hyperbolic law, like the Zipf's law power function, is often inadequate to describe rank-size relationships. An alternative theoretical distribution is proposed based on theoretical physics arguments starting from the Yule-Simon distribution. A modeling is proposed leading to a universal form. A theoretical suggestion for the best (or optimal) distribution, is provided through an entropy argument. The ranking of areas through the number of cities in various countries and some sport competition ranking serves for the present illustrations.
A universal rank-size law / Cerqueti, Roy; Ausloos, Marcel. - In: PLOS ONE. - ISSN 1932-6203. - 11(11), e0166011:(2016), pp. 1-15. [10.1371/journal.pone.0166011]
A universal rank-size law
Cerqueti Roy;
2016
Abstract
A mere hyperbolic law, like the Zipf's law power function, is often inadequate to describe rank-size relationships. An alternative theoretical distribution is proposed based on theoretical physics arguments starting from the Yule-Simon distribution. A modeling is proposed leading to a universal form. A theoretical suggestion for the best (or optimal) distribution, is provided through an entropy argument. The ranking of areas through the number of cities in various countries and some sport competition ranking serves for the present illustrations.File | Dimensione | Formato | |
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