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A Rank-Based Approach to Zipf's Law

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  • Ricardo T. Fernholz
  • Robert Fernholz

Abstract

An Atlas model is a rank-based system of continuous semimartingales for which the steady-state values of the processes follow a power law, or Pareto distribution. For a power law, the log-log plot of these steady-state values versus rank is a straight line. Zipf's law is a power law for which the slope of this line is -1. In this note, rank-based conditions are found under which an Atlas model will follow Zipf's law. An advantage of this rank-based approach is that it provides information about the dynamics of systems that result in Zipf's law.

Suggested Citation

  • Ricardo T. Fernholz & Robert Fernholz, 2016. "A Rank-Based Approach to Zipf's Law," Papers 1602.08533, arXiv.org.
    • Handle: RePEc:arx:papers:1602.08533
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    References listed on IDEAS

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