A universal rank-size law

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.

17 pages, 7 figures, 2 Tables, 49 references

References in corpus (7)

• Nonuniversal power law scaling in the probability distribution of scientific citations
• Numerical indications of a q-generalised central limit theorem
• Evidence of Economic Regularities and Disparities of Italian Regions From Aggregated Tax Income Size Data
• Beyond Zipf's Law: The Lavalette Rank Function and its Properties
• Two-exponent Lavalette function. A generalization for the case of adherents to a religious movement
• Ranking structures and Rank-Rank Correlations of Countries. The FIFA and UEFA cases
• Toward fits to scaling-like data, but with inflection points & generalized Lavalette function

Cited by in corpus (8)

• A joint text mining-rank size investigation of the rhetoric structures of the US Presidents' speeches
• Universal City-size distributions through rank ordering
• Exploring the Level of Urbanization Based on Zipf's Scaling Exponent
• Earthquakes economic costs through rank-size laws
• Words ranking and Hirsch index for identifying the core of the hapaxes in political texts
• Rank-size law, financial inequality indices and gain concentrations by cyclist teams. The case of a multiple stage bicycle race, like Tour de France
• Hagiotoponyms in France: Saint popularity, like a herding phase transition
• Markov Chain Monte Carlo for generating ranked textual data