Curve-fitting of frequency distributions of dependency distances in a multi-lingual parallel corpus

Curve-fitting of frequency distributions of dependency distances in a multi-lingual parallel corpus Masanori Oya School of Global Japanese Studies, Meiji University, 4-21-1, Nakano, Tokyo, Japan masanori_oya2019@meiji.ac.jp Abstract This study discusses the curve-fitting results of the frequency distributions of dependency distances in sentences from a multi-lingual parallel corpus. It assumes that these distributions fit a mathematically well-defined distribution (the right truncated modified Zipf- Alekseev distribution) quite well, which indicates that these distributions of dependency distances reflect an aspect of the universal properties of natural language. However, the results of the curve-fitting of frequency distributions of the dependency distances of different dependency types do not demonstrate a suitable fit to the right truncated modified Zipf-Alekseev distribution, suggesting the necessity of further research. 1 Introduction Dependency distance has been the center of focus of research on memory burden and syntactic complexity (Gibson, 1998, 2000; Gildea & Temperley, 2010; Grodner & Gibson, 2005; Li & Yan, 2021; Liu, 2007, 2008; Liu et al., 2017; Oya, 2013, 2021). The dependency distance between words in a dependency relation can be easily calculated; for example, in the sentence “Sarah has written an article in two months,” the noun Sarah depends on the auxiliary verb has as the subject, and the dependency distance between them is one. The noun article depends on written as its object, and the dependency distance between them is two. Dependency distance has been argued as an aspect of the universal properties of natural languages; more specifically, shorter dependency distances are preferred to longer ones, possibly due to the upper bound of the short-term memory of humans (Gibson, 2000). It has been found out that the threshold of dependency distance is four across different natural languages (Liu, 2008; Oya, 2021). This means that the frequencies of dependency distances one, two, or three are much higher than the frequencies of dependency distances four or larger. When we plot the frequency distributions of dependency distances on an x-y plane with the x axis being the dependency distance and the y axis its frequency, then the graph has a long tail to the right. In this context, frequency distributions of dependency distances have been discovered to fit the right truncated modified Zipf-Alekseev distribution (henceforth ZA distribution) quite well (Jiang & Liu, 2015; Liu, 2009; Ouyang & Jiang, 2017). The ZA distribution formula is illustrated below (Ouyang & Jiang, 2017; Popescu et al., 2014; Li and Yan, 2021): In the formula above, x is a dependency distance, y is its frequency, c is a constant, and the parameters a and b vary along with the fitness of the distributions of the frequencies. According to Li and Yan (2021), when the ZA distribution was fitted to the frequency distribution of dependency distances across essays written by Japanese EFL learners of different proficiencies, the results of good fitness were obtained. Figure 1. Frequency distributions of the dependency distances of Lower, Middle and High groups (Li & Yan, 2021, p.180) Li and Yan (2021) also found out that learner proficiencies are …

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