{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/corrections-of-zipf-s-and-heaps-laws-derived","title":"Corrections of Zipf's and Heaps' Laws Derived from Hapax Rate Models","arxiv_id":"2307.12896","date":"2023-07-24","proceeding":null,"authors":["Łukasz Dębowski"],"abstract":"The article introduces corrections to Zipf's and Heaps' laws based on systematic models of the proportion of hapaxes, i.e., words that occur once. The derivation rests on two assumptions: The first one is the standard urn model which predicts that marginal frequency distributions for shorter texts look as if word tokens were sampled blindly from a given longer text. The second assumption posits that the hapax rate is a simple function of the text length. Four such functions are discussed: the constant model, the Davis model, the linear model, and the logistic model. It is shown that the logistic model yields the best fit.","url_abs":"https://arxiv.org/abs/2307.12896v4","url_pdf":"https://arxiv.org/pdf/2307.12896v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"corrections-of-zipf-s-and-heaps-laws-derived","repo_url":"https://github.com/lukasz-debowski/zipfanatomy","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"corrections-of-zipf-s-and-heaps-laws-derived","repo_url":"https://github.com/lukasz-debowski/zipfanatomy4journal","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}