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A Universal Rank-Size Law.

Marcel Ausloos1,2, Roy Cerqueti3

  • 1School of Business, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom.

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|November 5, 2016
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Summary
This summary is machine-generated.

This study proposes a new universal distribution model to better describe rank-size relationships than Zipf's law. The optimal distribution is suggested using entropy arguments and illustrated with city and sports rankings.

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Area of Science:

  • Theoretical Physics
  • Statistical Distributions
  • Complex Systems

Background:

  • Zipf's law, a hyperbolic power function, often fails to adequately capture rank-size distribution complexities.
  • Existing models may not fully represent the underlying mechanisms driving these relationships.

Purpose of the Study:

  • To propose an alternative theoretical distribution for rank-size relationships.
  • To develop a universal model derived from theoretical physics principles.
  • To identify the optimal distribution using entropy arguments.

Main Methods:

  • Utilizing the Yule-Simon distribution as a foundation for theoretical physics arguments.
  • Developing a modeling approach to achieve a universal distribution form.
  • Applying entropy arguments to determine the optimal distribution.

Main Results:

  • A novel theoretical distribution is proposed as an improvement over hyperbolic laws like Zipf's law.
  • A universal form for the distribution has been modeled.
  • An entropy-based argument provides a theoretical basis for the 'best' or optimal distribution.

Conclusions:

  • The proposed distribution offers a more robust framework for analyzing rank-size relationships.
  • The universal model and entropy-based optimality provide new insights into complex system rankings.
  • Illustrative examples using city populations and sports rankings validate the proposed approach.