{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:38:36Z","timestamp":1760143116394,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T00:00:00Z","timestamp":1704931200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012579","name":"Natural Science Foundation of Qinghai Province","doi-asserted-by":"publisher","award":["2019-ZJ-920","12161072"],"award-info":[{"award-number":["2019-ZJ-920","12161072"]}],"id":[{"id":"10.13039\/501100012579","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of China","award":["2019-ZJ-920","12161072"],"award-info":[{"award-number":["2019-ZJ-920","12161072"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Parameter estimation is an important component of statistical inference, and how to improve the accuracy of parameter estimation is a key issue in research. This paper proposes a linear Bayesian estimation for estimating parameters in a misrecorded Poisson distribution. The linear Bayesian estimation method not only adopts prior information but also avoids the cumbersome calculation of posterior expectations. On the premise of ensuring the accuracy and stability of computational results, we derived the explicit solution of the linear Bayesian estimation. Its superiority was verified through numerical simulations and illustrative examples.<\/jats:p>","DOI":"10.3390\/e26010062","type":"journal-article","created":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T05:24:12Z","timestamp":1704950652000},"page":"62","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Linear Bayesian Estimation of Misrecorded Poisson Distribution"],"prefix":"10.3390","volume":"26","author":[{"given":"Huiqing","family":"Gao","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistic, Qinghai Normal University, Xining 810008, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3326-8663","authenticated-orcid":false,"given":"Zhanshou","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistic, Qinghai Normal University, Xining 810008, China"},{"name":"The State Key Laboratory of Tibetan Intelligent Information Processing and Application, Xining 810008, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fuxiao","family":"Li","sequence":"additional","affiliation":[{"name":"Faculty of Science, Xi\u2019an University of Technology, Xi\u2019an 710048, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1080\/01621459.1960.10482054","article-title":"Estimating the parameters of a modified Poisson distribution","volume":"55","author":"Cohen","year":"1960","journal-title":"J. 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