Possible origin of power-law behavior in n-tuple Zipf analysis

András Czirók, H. Eugene Stanley, and Tamás Vicsek
Phys. Rev. E 53, 6371 – Published 1 June 1996
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Abstract

In n-tuple Zipf analysis, "words" are defined as strings of n digits, and their normalized frequency of occurrence ω is measured for a given "text" (sequence of digits). In the case of various non-Markovian sequences, the probability density of the frequencies P(ω) has a power-law tail. Here we argue that a broad class of unbiased binary texts exhibiting a nonexponential distribution of cluster sizes can indeed yield a power-law behavior of P(ω), where we define clusters to be strings of identical digits. We support this result by numerical studies of long-range correlated sequences generated by three different methods that result in nonexponential cluster-size distribution: inverse Fourier transformation, Lévy walks, and the expansion-modification system. Our calculations shed light on the possible connection between the Zipf plot and the non-Markovian nature of the text: as the long-range correlations become dominant, the probability of the appearance of long clusters is increased, leading to the observed "scaling" in the Zipf plot.

  • Received 27 October 1995

DOI:https://doi.org/10.1103/PhysRevE.53.6371

©1996 American Physical Society

Authors & Affiliations

András Czirók1,2,*, H. Eugene Stanley1, and Tamás Vicsek2

  • 1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215
  • 2Department of Atomic Physics, Eötvös University, Budapest, Puskin utca 5-7, 1088 Hungary

  • *Electronic address: czirok@hercules.elte.hu

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Vol. 53, Iss. 6 — June 1996

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