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Rank-frequency distribution of natural languages: A difference of probabilities approach

Author

Listed:
  • Cocho, Germinal
  • Rodríguez, Rosalío F.
  • Sánchez, Sergio
  • Flores, Jorge
  • Pineda, Carlos
  • Gershenson, Carlos

Abstract

In this paper we investigate the time variation of the rank k of words for six Indo-European languages using the Google Books N-gram Dataset. Based on numerical evidence, we regard k as a random variable whose dynamics may be described by a Fokker–Planck equation which we solve analytically. For low ranks the distinct languages behave differently, maybe due to the syntax rules, whereas for k>50 the law of large numbers predominates. We analyze the frequency distribution of words using the data and their adjustment in terms of time-dependent probability density distributions. We find small differences between the data and the fits due to conflicting dynamic mechanisms, but the data show a consistent behavior with our general approach. For the lower ranks the behavior of the data changes among languages presumably, again, due to distinct dynamic mechanisms. We discuss a possible origin of these differences and assess the novel features and limitations of our work.

Suggested Citation

  • Cocho, Germinal & Rodríguez, Rosalío F. & Sánchez, Sergio & Flores, Jorge & Pineda, Carlos & Gershenson, Carlos, 2019. "Rank-frequency distribution of natural languages: A difference of probabilities approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 532(C).
    • Handle: RePEc:eee:phsmap:v:532:y:2019:i:c:s0378437119310507
    DOI: 10.1016/j.physa.2019.121795
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