A growth model that generates an n-tuple Zipf law

Xiaocong Gan, Dahui Wang and Zhangang Han

Physica A: Statistical Mechanics and its Applications, 2011, vol. 390, issue 5, 792-800

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.

Keywords: Zipf law; n-tuple; n-gram; Simon’s model; Preferential selection (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:390:y:2011:i:5:p:792-800

DOI: 10.1016/j.physa.2010.11.001

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