{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T05:47:22Z","timestamp":1777009642245,"version":"3.51.4"},"reference-count":36,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,14]],"date-time":"2025-03-14T00:00:00Z","timestamp":1741910400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Poisson regression is used to model count response variables. The method has a strict assumption that the mean and variance of the response variable are equal, while, in practice, the case of overdispersion is common. Also, in multicollinearity, the model parameter estimates obtained with the maximum likelihood estimator are adversely affected. This paper introduces a new biased estimator that extends the modified Kibria\u2013Lukman estimator to the Poisson\u2013Inverse-Gaussian regression model to deal with overdispersion and multicollinearity in the data. The superiority of the proposed estimator over the existing biased estimators is presented in terms of matrix and scalar mean square error. Moreover, the performance of the proposed estimator is examined through a simulation study. Finally, on a real dataset, the superiority of the proposed estimator over other estimators is demonstrated.<\/jats:p>","DOI":"10.3390\/a18030169","type":"journal-article","created":{"date-parts":[[2025,3,14]],"date-time":"2025-03-14T13:07:51Z","timestamp":1741957671000},"page":"169","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["An Alternative Estimator for Poisson\u2013Inverse-Gaussian Regression: The Modified Kibria\u2013Lukman Estimator"],"prefix":"10.3390","volume":"18","author":[{"given":"Rasha A.","family":"Farghali","sequence":"first","affiliation":[{"name":"Department of Mathematics, Insurance, and Applied Statistics, Helwan University, Cairo 11795, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2881-1297","authenticated-orcid":false,"given":"Adewale F.","family":"Lukman","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of North Dakota, Grand Forks, ND 58202, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0229-7958","authenticated-orcid":false,"given":"Zakariya","family":"Algamal","sequence":"additional","affiliation":[{"name":"Department of Statistics and Informatics, University of Mosul, Mosul 41002, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6335-3044","authenticated-orcid":false,"given":"Murat","family":"Genc","sequence":"additional","affiliation":[{"name":"Department of Management Information Systems, Faculty of Economics and Administrative Sciences, Tarsus University, 33400 Mersin, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hend","family":"Attia","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Insurance, and Applied Statistics, Helwan University, Cairo 11795, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,14]]},"reference":[{"key":"ref_1","first-page":"18","article-title":"The Poisson inverse Gaussian (PIG) generalized linear regression model for analyzing motor vehicle crash data","volume":"8","author":"Zha","year":"2015","journal-title":"J. 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