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Maximum Entropy, Word-Frequency, Chinese Characters, and Multiple Meanings

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  • Xiaoyong Yan
  • Petter Minnhagen

Abstract

The word-frequency distribution of a text written by an author is well accounted for by a maximum entropy distribution, the RGF (random group formation)-prediction. The RGF-distribution is completely determined by the a priori values of the total number of words in the text (M), the number of distinct words (N) and the number of repetitions of the most common word (kmax). It is here shown that this maximum entropy prediction also describes a text written in Chinese characters. In particular it is shown that although the same Chinese text written in words and Chinese characters have quite differently shaped distributions, they are nevertheless both well predicted by their respective three a priori characteristic values. It is pointed out that this is analogous to the change in the shape of the distribution when translating a given text to another language. Another consequence of the RGF-prediction is that taking a part of a long text will change the input parameters (M, N, kmax) and consequently also the shape of the frequency distribution. This is explicitly confirmed for texts written in Chinese characters. Since the RGF-prediction has no system-specific information beyond the three a priori values (M, N, kmax), any specific language characteristic has to be sought in systematic deviations from the RGF-prediction and the measured frequencies. One such systematic deviation is identified and, through a statistical information theoretical argument and an extended RGF-model, it is proposed that this deviation is caused by multiple meanings of Chinese characters. The effect is stronger for Chinese characters than for Chinese words. The relation between Zipf’s law, the Simon-model for texts and the present results are discussed.

Suggested Citation

  • Xiaoyong Yan & Petter Minnhagen, 2015. "Maximum Entropy, Word-Frequency, Chinese Characters, and Multiple Meanings," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-19, May.
  • Handle: RePEc:plo:pone00:0125592
    DOI: 10.1371/journal.pone.0125592
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    Cited by:

    1. Yan, Xiaoyong & Minnhagen, Petter, 2016. "Randomness versus specifics for word-frequency distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 828-837.
    2. Yan, Xiaoyong & Minnhagen, Petter & Jensen, Henrik Jeldtoft, 2016. "The likely determines the unlikely," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 112-119.
    3. Yan, Xiaoyong & Minnhagen, Petter, 2018. "The dependence of frequency distributions on multiple meanings of words, codes and signs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 554-564.
    4. Yan, Xiaoyong & Yang, Seong-Gyu & Kim, Beom Jun & Minnhagen, Petter, 2018. "Benford’s law and first letter of words," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 305-315.

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