Non-Zipfian Distribution of Stopwords or Function Words and Subset Selection Models

Abstract:Stopwords and function words are relatively less informative for the content of a language and more often play a structural role in a sentence. Stopwords are ubiquitous words and may contain verbs, adjectives and adverbs. On the other hand, function words are strictly prepositions, conjunctions, pronouns, determiners, qualifiers, articles, interrogatives, and a limited number of auxiliary verbs. In contrast to the well known Zipf's law for rank-frequency plot for all words, the rank-frequency plots for stopwords or function words are best fitted by the Beta Rank Function (BRF). On the other hand, the rank-frequency plots of non-stopwords or non-function-words also deviate from the Zipf's law, but are better described by a quadratic function of log-token-count over log-rank than by BRF. Based on the observed rank of stopwords or function words in the full word list, we propose a stopword/function word/subset selection model that the probability for being selected, as a function of the word's rank $r$, is a decreasing Hill's function ($1/(1+(r/r_{mid})^\gamma)$); whereas the probability for not being selected is the standard Hill's function ($1/(1+(r_{mid}/r)^\gamma)$). We validate this selection probability model by a direct estimation from an independent collection of texts. We also show analytically that this model leads to a BRF rank-frequency distribution for stopwords or function words when the original full word list follows the Zipf's law, as well as explaining the quadratic fitting function for the non-stopwords or non-function-words. A corollary of these results is that Zipf's law is not expected to be true for telegraphic speech in early childhood language learners or in agrammatism patients.

Computation and Language (cs.CL)

arXiv:2603.04691 [cs.CL]

(or arXiv:2603.04691v2 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2603.04691 Focus to learn more arXiv-issued DOI via DataCite

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