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A growth model that generates an n-tuple Zipf law

Author

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  • Gan, Xiaocong
  • Wang, Dahui
  • Han, Zhangang

Abstract

The n-tuple Zipf law widely exists in real symbol sequences such as DNA and language. Based on the n-tuple Zipf analysis on a vast amount of empirical data, we propose a model that can generate sequences with n-tuple Zipf features. In simple words, it is an iterative copy and paste process: repeatedly select a random subsequence from the current sequence and attach it to the end. Numerical results of our model show that the n-tuple Zipf law exists in our model generated data. We give detailed analytical derivations of our model, and get two estimation equations: the Zipf exponent and the minimal length of n-tuple for Zipf law to appear. Our model can also reproduce the symmetry breaking process of ATGC number differences in DNA data.

Suggested Citation

  • Gan, Xiaocong & Wang, Dahui & Han, Zhangang, 2011. "A growth model that generates an n-tuple Zipf law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(5), pages 792-800.
  • Handle: RePEc:eee:phsmap:v:390:y:2011:i:5:p:792-800
    DOI: 10.1016/j.physa.2010.11.001
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