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Maximum Entropy, Word-Frequency, Chinese Characters, and Multiple Meanings
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
(k_max). 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, k_max) 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, k_max), 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.Comment: 15 pages, 10 figures, 2 table
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