{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T13:36:57Z","timestamp":1773668217399,"version":"3.50.1"},"reference-count":28,"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\/501100007345","name":"King Mongkut\u2019s University of Technology North Bangkok","doi-asserted-by":"publisher","award":["KMUTNB-67-BASIC-16"],"award-info":[{"award-number":["KMUTNB-67-BASIC-16"]}],"id":[{"id":"10.13039\/501100007345","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The inverse Gaussian distribution, known for its flexible shape, is widely used across various applications. Existing confidence intervals for the mean parameter, such as profile likelihood, reparametrized profile likelihood, and Wald-type reparametrized profile likelihood with observed Fisher information intervals, are generally effective. However, our simulation study identifies scenarios where the coverage probability falls below the nominal confidence level. Wald-type intervals are widely used in statistics and have a symmetry property. We mathematically derive the Wald-type profile likelihood (WPL) interval and the Wald-type reparametrized profile likelihood with expected Fisher information (WRPLE) interval and compare their performance to existing methods. Our results indicate that the WRPLE interval outperforms others in terms of coverage probability, while the WPL typically yields the shortest interval. Additionally, we apply these proposed intervals to a real dataset, demonstrating their potential applicability to other datasets that follow the IG distribution.<\/jats:p>","DOI":"10.3390\/sym16010093","type":"journal-article","created":{"date-parts":[[2024,1,11]],"date-time":"2024-01-11T08:27:07Z","timestamp":1704961627000},"page":"93","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Wald Intervals via Profile Likelihood for the Mean of the Inverse Gaussian Distribution"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9925-9615","authenticated-orcid":false,"given":"Patchanok","family":"Srisuradetchai","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-5121-0849","authenticated-orcid":false,"given":"Ausaina","family":"Niyomdecha","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6082-4779","authenticated-orcid":false,"given":"Wikanda","family":"Phaphan","sequence":"additional","affiliation":[{"name":"Department of Applied Statistics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"},{"name":"Research Group in Statistical Learning and Inference, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1111\/j.2517-6161.1978.tb01039.x","article-title":"The Inverse Gaussian Distribution and Its Statistical Application\u2014A Review","volume":"40","author":"Folks","year":"1978","journal-title":"J. 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