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This innovative distribution offers flexibility by accommodating an arbitrary number of inflation points at various locations. The paper explores key distributional properties associated with this modified distribution. Additionally, this study proposes several estimators designed to obtain estimates for the unknown parameters. Furthermore, the paper introduces a new count regression model that utilizes the modified distribution. To assess the performance of the proposed distribution and the count regression model, a comprehensive Monte Carlo simulation study is conducted. In the final stage of the paper, a real-world dataset is scrutinized to ascertain the superiority of the proposed model. This empirical analysis contributes to validating the practical applicability and effectiveness of the newly introduced distribution in comparison to existing models.<\/jats:p>","DOI":"10.1007\/s00500-024-09889-4","type":"journal-article","created":{"date-parts":[[2024,7,26]],"date-time":"2024-07-26T17:05:15Z","timestamp":1722013515000},"page":"10911-10928","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Multiple arbitrarily inflated negative binomial regression model and its application"],"prefix":"10.1007","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6255-1268","authenticated-orcid":false,"given":"Ihab","family":"Abusaif","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Co\u015fkun","family":"Ku\u015f","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,7,26]]},"reference":[{"key":"9889_CR1","doi-asserted-by":"crossref","unstructured":"Abusaif I, Ku\u015f C (2023) Multiple arbitrarily inflated poisson regression analysis. 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The authors certify that they have NO affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers\u2019 bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This is to state that we (Authors) give full permission for the publication, and reproduction in publication (including books, journals, online and internet). I declare, in consequence of granting this permission, that I have no claim on the ground of breach of confidence or any other ground in any legal system against the authors. I hereby agree to release and discharge authors and any editors or other contributors and their agents, publishers, successors and assigns from any claims, demands, or causes of action that I may now have or may hereafter have for libel, defamation, invasion of privacy, copyright or moral rights or violation of any other rights.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Informed consent"}}]}}