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.
CitationPLoS ONE 11(11): e0166011.
Author affiliation/Organisation/COLLEGE OF SOCIAL SCIENCES, ARTS AND HUMANITIES/School of Management
VersionVoR (Version of Record)
Published inPLoS ONE 11(11): e0166011.
PublisherPublic Library of Science
NotesData Availability: Our datasets are public and freely available. Two datasets concern ranked countries, even in different sport competitions contexts: Olympic Games in Bejing 2008 and London 2012; soccer federations affiliated to the FIFA. The third dataset is associated of the ranking of provinces in four countries Belgium, Bulgaria, France, Italy (BE, BG, FR, IT) under the criterion of the number of municipalities. Data sources for the new illustrations have been included clearly in the revised version of the paper: for the Olympic Games, see http://www.bbc.co.uk/sport/olympics/2012/medals/countries; for the FIFA, see http://www.fifa.com/ and for how the FIFA ranking coefficient is calculated, see http://www.fifa.com/worldranking/procedureandschedule/menprocedure/index.html. For what concerns the administrative structure of BE, BG, FR, IT, we specify a reference year (2011) to exclude the possibility of biases in the replication of the analysis due to administrative changes.