{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T20:08:43Z","timestamp":1769198923192,"version":"3.49.0"},"reference-count":14,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T00:00:00Z","timestamp":1768953600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Portuguese Foundation for Science and Technology","award":["UIDB\/00212\/2020"],"award-info":[{"award-number":["UIDB\/00212\/2020"]}]},{"name":"Portuguese Foundation for Science and Technology","award":["UIDB\/04630\/2020"],"award-info":[{"award-number":["UIDB\/04630\/2020"]}]},{"name":"Portuguese Foundation for Science and Technology","award":["UIDB\/00297\/2020"],"award-info":[{"award-number":["UIDB\/00297\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The New Polynomial Exponential Distribution (NPED), introduced by Beghriche et al. (2022), provides a flexible one-parameter family capable of representing diverse hazard shapes and heavy-tailed behavior. Regression frameworks based on the NPED, however, have not yet been established. This paper introduces two methodological extensions: (i) a generalized linear model (NPED-GLM) in which the distribution parameter depends on covariates, and (ii) a Poisson\u2013NPED count regression model suitable for overdispersed and heavy-tailed count data. Likelihood-based inference, asymptotic properties, and simulation studies are developed to investigate the performance of the estimators. Applications to engineering failure-count data and insurance claim frequencies illustrate the advantages of the proposed models relative to classical Poisson, negative binomial, and Poisson\u2013Lindley regressions. These developments substantially broaden the applicability of the NPED in actuarial science, reliability engineering, and applied statistics.<\/jats:p>","DOI":"10.3390\/computation14010026","type":"journal-article","created":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T11:11:17Z","timestamp":1768993877000},"page":"26","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Regression Extensions of the New Polynomial Exponential Distribution: NPED-GLM and Poisson\u2013NPED Count Models with Applications in Engineering and Insurance"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4759-5529","authenticated-orcid":false,"given":"Halim","family":"Zeghdoudi","sequence":"first","affiliation":[{"name":"Laboratory of Probability and Statistics (LaPS), Badji Mokhtar-Annaba University, Annaba 23000, Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9209-7772","authenticated-orcid":false,"given":"Sandra S.","family":"Ferreira","sequence":"additional","affiliation":[{"name":"Mathematics Department, University of Beira Interior, 6201-001 Covilh\u00e3, Portugal"},{"name":"Centre of Mathematics and Applications, University of Beira Interior, 6201-001 Covilh\u00e3, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3815-2312","authenticated-orcid":false,"given":"Vinoth","family":"Raman","sequence":"additional","affiliation":[{"name":"Deanship of Quality and Academic Accreditation, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam 31441, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9095-0947","authenticated-orcid":false,"given":"D\u00e1rio","family":"Ferreira","sequence":"additional","affiliation":[{"name":"Mathematics Department, University of Beira Interior, 6201-001 Covilh\u00e3, Portugal"},{"name":"Centre of Mathematics and Applications, University of Beira Interior, 6201-001 Covilh\u00e3, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Cameron, A.C., and Trivedi, P.K. (2013). Regression Analysis of Count Data, Cambridge University Press. [2nd ed.].","DOI":"10.1017\/CBO9781139013567"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Hilbe, J.M. (2011). Negative Binomial Regression, Cambridge University Press. [2nd ed.].","DOI":"10.1017\/CBO9780511973420"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1111\/j.1751-5823.2005.tb00250.x","article-title":"Mixed Poisson distributions","volume":"73","author":"Karlis","year":"2005","journal-title":"Int. Stat. Rev."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"209","DOI":"10.2307\/3314912","article-title":"Negative binomial and mixed Poisson regression","volume":"15","author":"Lawless","year":"1987","journal-title":"Can. J. Stat."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"274","DOI":"10.28951\/bjb.v41i3.635","article-title":"Counting models for overdispersed data: A review with applications","volume":"41","author":"Azevedo","year":"2023","journal-title":"Biom. Bras. J."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Alomair, G., Tajuddin, R.R.M., Bakouch, H.S., and Almohisen, A. (2024). 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