Character Distributions of Classical Chinese Literary Texts: Zipf’s Law, Genres, and Epochs

paper, specified "short paper"
  1. 1. Chao-Lin Liu

    National Chengchi University

  2. 2. Shuhua Zhang

    Harvard University

  3. 3. Yuanli Geng

    Harvard University

  4. 4. Huei-ling Lai

    National Chengchi University

  5. 5. Hongsu (Henry) Wang

    Harvard University

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Introduction and Main Findings

Chinese characters are the basic units for Chinese words, and a Chinese word can include one, two, or

more characters. Many characters can function as

words in Chinese. For instance, “AÍ” represents “humanities”, and “A” and “A” are characters that carry their own meanings. Words that contain two, three, and more characters can be referred as bigrams, trigrams and other appropriate names for n-grams. Chinese does not separate words with spaces like English, so a reader must “segment” a character string into words to understand Chinese statements.

Mandarin Chinese has evolved over the past thousands of years (Yong and Peng 2008). Documents written in current vernacular Chinese contain a large number of bigrams and trigrams, while texts of classical Chinese (sometimes referred to as “literary Chinese”) contain many more unigrams. In the Academica Sinica Balanced Corpus (ASBC), unigrams contribute only 2.1% of word types, but constitute a 44.8% share of word tokens (“types” refers to distinct words in linguistics, e.g., “today is today” has three tokens and two types). In contrast, bigrams and trigrams together constitute 82% and 53% of the word types and tokens, respectively.

Zipf discovered that the relative frequencies of words are inversely proportional to their ranks in

Chinese and English documents (Zipf, 1932) in his

endeavor to establish a theory of Principle of Least Effort (Zipf, 1949). Many researchers have attempted to find the parameters in the Zipf-Mandelbrot distributions (see also, Piantadosi, 2015) for English and for Chinese (see Ha et al, 2003) many have explored extensions and applications of the law (see Altmann et al, 2002).

Previous research works for Chinese have focused mainly on fitting the Zipfian distributions to Chinese corpora. Some considered a distributed sample of corpora (Altmann et al, 2002), and others confined their analysis to a specific corpus (Deng et al, 2014). Some researchers have pondered on explanations for why the statistics of languages obey the Zipfian distributions (Powers, 1998, and Piantadosi, 2015). We examined the Zipfian distributions of 14 collections of Chinese texts that were published from 1046BC (the year when the Zhou Dynasty of

China began) to 2007AD, and we found that the genres and epochs of the collections influence the distributions. The majority of our collections are poetic works written in classical Chinese. We also included official documents of the Tang Dynasty, novels of the Ming and Qing dynasties, and news articles of modern days.

The character distributions for the corpora of poems of 618-1644AD (the period stretching from the Tang dynastry to the Ming dynasty) exhibit strikingly similar Zipfian distributions. In contrast, the character distributions of the three genres of corpora that were all written in the Tang dynasty are distinguishable, although the characters frequently which are used in these documents are very similar. The word distribution of the ASBC differs significantly from other character distributions, indicating the importance of differentiating character- and word-based models of Chinese.

Corpora and Comparisons

For ease of references, we assigned an acronym for each of the 14 corpora, and show their names in Chinese (Collection) and periods of publication (Time) in Table 1.

















Before 589AD




















ca. 16th century



ca. 18,h century




Table 1. The corpora used in this study include texts published during 1046BC-2007AD.

The corpora consist of representative literature that has been published since 1046BC. In particular, we have at least one collection for each of the major dynasties that existed before 1644AD. The majority of our collections are of poetic works (we consider SJ, CV,

HF, PT, CTP, CSP, CSL, YSX, and LCSJ collections of poetic works) which fact lends itself to the study of the effects of genres on the character distributions. A collection of poetic works for the Qing Dynasty (which lasted from 1644 to 1912AD) is unavailable because an editorial committee is still working on its production (Zhu, 1994).

The corpora contain more than 42 million characters, excluding the punctuation marks that were added into the corpora by the data providers. When counting the characters, we also exclude characters that cannot be shown on ordinary computers. The frequencies of such rare and obsolete characters are not large, so ignoring them will not affect the statistical properties reported in this study.

Only the ASBC was segmented and the segmentation was verified by human experts. Hence, we can inspect its character and word distributions. The other corpora were written in classical Chinese and we do not have a reliable way for segmentation, so we will only analyze the character distributions.

We created charts that are based on the typical form of Zipf's law:

log(fw)) = k -alog(r(w))
where w, f(w), and r(w) denote a word, its frequency, and rank in a corpus, respectively. The rank of the most

frequent word in a corpus is 1. N is the size of the

corpus, and k and @ are constants.

Observations and Discussions: Influences of Genres and Epochs

The generalizability of the Zipf's law is the main

reason that it has attracted the attention of many researchers. It can be applied to various natural distributions including those of part-of-speech of words (Wang et al, 2012), city sizes (Anderson and Ge, 2005), and corporal revenues (Chen et al, 2008).

Figure 1 shows the Zipfian curves when we consider the character distributions of all of the 14 corpora. We intentionally plot the curves in one chart, although this makes the individual curves undistinguishable. Although the curves are not linear, which is common as reported in the literature, the curves show a consistent trend, suggesting a common regularity that is shared by Chinese texts that were produced over the period of 3000 years.


Figure 1. Zipfian curves of 14 corpora suggest a common trend. (Character distributions)

Instead of treating the 14 corpora as a single corpus to fit the resulting distribution for Zipf's law, we examined the curves to investigate possible factors

that influenced the positions of the curves. In Figure 2,

we show the curves of lyrics ("¡t^” /ci2/) and poems ("a^” /shil/. The left halves of the curves overlap almost perfectly, which strongly indicates that the poetic works share very close statistical characteristics.

Table 2 lists ten most frequent characters found in each of the corpora and for which the curves are plotted in Figure 2.

The lists are very similar, and, out of the 60 characters in Table 2, there are only 16 distinct characters (some of which are homonyms, for which only one pronunciation is provided). In fact, we can compare the most frequent characters of any two corpora, e.g., the CTP and the CSP, to further investigate their similarity (Chen et al, 2012), and we found that the most frequent 1700 characters in the CTP and the CSP are the same characters.

Not all of the corpora of poetic works have similar curves. We added the curves for the SJ, CV, and HF in Figure 3, and it is evident that these new curves do not overlap with those in Figure 2 very well. The poetic works in the SJ, CV, and HF were produced very much earlier than those listed in Figure 2.

Figure 3. Curves for ancient poetic works (SJ, CV, and HF) do not coincide with those of later poems.

While the time of the production of the corpora affects the Zipfian curves, the curves for corpora that were produced in the same dynasty may not be the same. The CTW, MZM, and CTP are three different types of works that were all produced in the Tang Dynasty. We compared the most frequent characters shared by the CTP and CTW, and found that the sets of their most frequent 2000 characters differ only in three characters. Despite such an extreme overlap, their curves in Figure 4 suggest that genre affects the character distributions.

Figure 4. Curves of corpora that belong to the same dynasty but of different genres deviate from each other.

Given the above observations, one may have expected that the curves for the novels that were published in the 16th and 18th centuries, i.e., the JTTW and DRC, will deviate from the curves for the earlier poems, as the curves in Figure 5 show.

Figure 5. Curves of corpora that contain novels of 16th and 18th century (JTTW & DRC, respectively) deviate from the curves in Figure 2.

Character vs. Word distributions

We considered the character distribution when we analyzed the contents of the ASBC in Figure 1, where we found that the character distributions of the vernacular and classical Chinese texts show a reasonable common trend. The ASBC contains documents that were written in vernacular Chinese, so we must also analyze its word distribution, and Figure 6 shows the curves for both the character and word distributions.

A chart like that of Figure 6 can mislead one to infer that Chinese texts do not conform to Zipf's law. It is well accepted that the number of Chinese characters is limited, although there is no consensus about the exact number of characters. In contrast, there is virtually no limit on the number of legal Chinese n-grams. As a result, the sharp downturn of the character distribution and the intersection of the two curves in Figure 6 are expected, and this can be observed in languages other than Chinese in some special settings (Montemurro, 2001). We should examine the Zipfian curves on the same basis, e.g., character or word, while considering cultural factors that may influence actual language usage.

Figure 6. Word and character distributions for the ASBC differ significantly.

Concluding Remarks

We have judged the similarity between the Ziphian curves based on the visual closeness, though we can quantify the degree of similarity when desired (Hu and Kuo, 2005). Researchers have noticed the deviations of Zipfian curves at the high- and low-frequency ends (Hu and Kuo, 2005, Rousseau and Zhang, 1992) and tried to find density functions that fit the data. The statistics at the high-frequency ends of the curves are evidently more reliable. We focused on the deviations at the high-frequency ends of the curves, and discussed how the deviations in these regions may relate to the genres and epochs of the corpora, employing the lists of most frequent characters of the corpora as extra supports.


This research was supported in part by the grant

104-2221-E-004-005-MY3 from the Ministry of Science and Technology of Taiwan, the grant USA-HAR-105-V02 from the Top University Strategic Alliance of Taiwan, and the Senior Fulbright Research Grant 20162017.


Altmann, G., Best, K.-H., Hrebicek, L., Köhler, R., Kromer, V., Rottmann, O., Schulz, A., Wimmer, G., and Ziegler,

A. (Eds.) (2002) Glottometrics 5, RAM-Verlag.

Anderson, G. and Ge, Y. (2005). The size distribution of

Chinese cities, Regional Science and Urban Economics,


Chen, Q., Guo, J. , and Liu, Y. (2012). A statistical study on Chinese word and character usage in literatures from the

Tang dynasty to the present, Journal of Quantitative

Linguistics, 19(3):232-248.

Chen, Q., Zhang, J, and Wang, Y. (2008). The Zipf's law in the revenue of top 500 Chinese companies, Proc. of the Fourth Int'l Conf. on Wireless Communications, Networking and Mobile Computing.

Deng, W., Allahverdyan, A.E., Li, B., and Wang, Q.A. (2014).

Rank-frequency relation for Chinese characters, The European Physical Journal B, 87, article 47.

Ha, L.Q., Sicilia-Garcia, E.I., Ming, J., and Smith, F.J. (2003).

Extension of Zipf's law to word and character n-grams for English and Chinese, Int'l J. of Computational

Linguistics and Chinese Language Processing, 8(1):77-102

Hu, C.-K. and Kuo, W.-C.. (2005). Universality and scaling in the statistical data of literary works, POLA Forever: Festschrift in Honor of Professor William S.-Y. Wang on His 70th Birthday, Dah-an Ho and Ovid J. L. Tzeng (Eds.), 115139.

Montemurro, M.A. (2001). Beyond the Zipf-Mandelbrot law in quantitative linguistics, Physica A, 300:567-578.

Piantadosi, S.T.. (2015). Zipf's word frequency law in

natural language: A critical review and future directions,

Psychonomic Bulletin & Review, 21(5):1112-1130.

Powers, D.M.W. (1998). Applications and Explanations of Zipf's Law. Proceedings of the Workshop on New Methods in Language Processing and Computational Natural

Language Learning, 151-160.

Rousseau, R. and Zhang, Q. (1992). Zipf's data on the frequency of Chinese words Revised, Scientometrics,


Wang, D., Zhu, D., and Su, Z. (2012). Lotka phenomenon in

the words' syntactic distribution complexity,

Scientometrics, 90:483-498.

Yong, H. and Peng, J. (2008). Chinese Lexicography, Oxford University Press.

Zipf, G.K. (1932). Selected Studies of the Principle of Relative Frequency in Language, Harvard University Press.

Zipf, G.K. (1949). Human Behavior and the Principle of Least Effort: An Introduction of Human Ecology, Addison-Wesley Press

Zhu, Z. (^^fö). (1994). Establishing the editorial board for the Complete Qing Poems

Studies in Qing History 0(3):96. (in Chinese)

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Conference Info


ADHO - 2017

Hosted at McGill University, Université de Montréal

Montréal, Canada

Aug. 8, 2017 - Aug. 11, 2017

438 works by 962 authors indexed

Series: ADHO (12)

Organizers: ADHO