{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:53:24Z","timestamp":1760144004328,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,8]],"date-time":"2024-03-08T00:00:00Z","timestamp":1709856000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"This research was funded by King Mongkut\u2019s University of Technology North Bangkok, contract number: KMUTNB-PHD-63-01.","award":["KMUTNB-PHD-63-01."],"award-info":[{"award-number":["KMUTNB-PHD-63-01."]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Due to slash\/burn agricultural activity and frequent forest fires, PM2.5 has become a significant air pollution problem in Thailand, especially in the north and north east regions. Since its dispersion differs both spatially and temporally, estimating PM2.5 concentrations discretely by area, for which the inverse Gaussian distribution is suitable, can provide valuable information. Herein, we provide derivations of the simultaneous confidence interval for the ratios of the coefficients of variation of multiple inverse Gaussian distributions using the generalized confidence interval, the Bayesian interval based on the Jeffreys\u2019 rule prior, the fiducial interval, and the method of variance estimates recovery. The efficacies of these methods were compared by considering the coverage probability and average length obtained from simulation results of daily PM2.5 datasets. The findings indicate that in most instances, the fiducial method with the highest posterior density demonstrated a superior performance. However, in certain scenarios, the Bayesian approach using the Jeffreys\u2019 rule prior for the highest posterior density yielded favorable results.<\/jats:p>","DOI":"10.3390\/sym16030331","type":"journal-article","created":{"date-parts":[[2024,3,8]],"date-time":"2024-03-08T11:47:30Z","timestamp":1709898450000},"page":"331","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The Simultaneous Confidence Interval for the Ratios of the Coefficients of Variation of Multiple Inverse Gaussian Distributions and Its Application to PM2.5 Data"],"prefix":"10.3390","volume":"16","author":[{"given":"Wasana","family":"Chankham","sequence":"first","affiliation":[{"name":"Department of Applied Statistics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8269-3397","authenticated-orcid":false,"given":"Sa-Aat","family":"Niwitpong","sequence":"additional","affiliation":[{"name":"Department of Applied Statistics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3059-1131","authenticated-orcid":false,"given":"Suparat","family":"Niwitpong","sequence":"additional","affiliation":[{"name":"Department of Applied Statistics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1080\/00401706.1976.10489423","article-title":"Optimum test procedures for the mean of first passage time in Brownian motion with positive drift (inverse Gaussian distribution)","volume":"18","author":"Chhikara","year":"1976","journal-title":"Technometrics"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2301","DOI":"10.1016\/j.bpj.2018.10.030","article-title":"Analysis of NMR Spin Relaxation Data Using an Inverse Gaussian Distribution Function","volume":"115","author":"Hsu","year":"2018","journal-title":"Biophys. 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