{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T08:44:14Z","timestamp":1762159454833,"version":"build-2065373602"},"reference-count":45,"publisher":"Wiley","issue":"8","license":[{"start":{"date-parts":[[2025,7,29]],"date-time":"2025-07-29T00:00:00Z","timestamp":1753747200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271231","12001229","11901053"],"award-info":[{"award-number":["12271231","12001229","11901053"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007847","name":"Natural Science Foundation of Jilin Province","doi-asserted-by":"publisher","award":["20210101151JC"],"award-info":[{"award-number":["20210101151JC"]}],"id":[{"id":"10.13039\/100007847","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Quality &amp; Reliability Eng"],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Count time series frequently exhibit overdispersion (variance is greater than mean) in practice. The first\u2010order integer\u2010valued autoregressive (INAR(1)) process based on binomial thinning operator with Poisson\u2010geometric marginal distributions [6], namely PGINAR(1) model, is a powerful statistical model to fit overdispersed counts. However, the statistical inference and monitoring for the PGINAR(1) model has not received sufficient research. To deal with these problems, this article concentrates on the estimation methods and monitoring of mean shift for the PGINAR(1) model. The Yule\u2010Walker, conditional least squares, modified quasi\u2010likelihood, and conditional maximum likelihood methods are used to estimate the model parameters and several control charts are proposed to handle the monitoring problems. Simulation studies and a real data analysis are conducted to demonstrate the effectiveness of the PGINAR(1) model and related statistical\u00a0methods.<\/jats:p>","DOI":"10.1002\/qre.70032","type":"journal-article","created":{"date-parts":[[2025,7,29]],"date-time":"2025-07-29T18:35:17Z","timestamp":1753814117000},"page":"3491-3505","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Inference and Monitoring for the Poisson\u2010Geometric INAR(1) Model"],"prefix":"10.1002","volume":"41","author":[{"given":"Shuhui","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics Liaoning University Shenyang China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Danshu","family":"Sheng","sequence":"additional","affiliation":[{"name":"School of Mathematics Harbin Institute of Technology Harbin 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