{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:18:13Z","timestamp":1760149093843,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,5]],"date-time":"2023-07-05T00:00:00Z","timestamp":1688515200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Hebei Province","award":["A2020207006","A2022208001","CXZZSS2023103","12001155"],"award-info":[{"award-number":["A2020207006","A2022208001","CXZZSS2023103","12001155"]}]},{"name":"Foundation of Hebei Educational Department","award":["A2020207006","A2022208001","CXZZSS2023103","12001155"],"award-info":[{"award-number":["A2020207006","A2022208001","CXZZSS2023103","12001155"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["A2020207006","A2022208001","CXZZSS2023103","12001155"],"award-info":[{"award-number":["A2020207006","A2022208001","CXZZSS2023103","12001155"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Generalized logistic distribution, as the generalized form of the symmetric logistic distribution, plays an important role in reliability analysis. This article focuses on the statistical inference for the stress\u2013strength parameter R=P(Y&lt;X) of the generalized logistic distribution with the same and different scale parameters. Firstly, we use the frequentist method to construct asymptotic confidence intervals, and adopt the generalized inference method for constructing the generalized point estimators as well as the generalized confidence intervals. Then the generalized fiducial method is applied to construct the fiducial point estimators and the fiducial confidence intervals. Simulation results demonstrate that the generalized fiducial method outperforms other methods in terms of the mean square error, average length, and empirical coverage. Finally, three real datasets are used to illustrate the proposed methods.<\/jats:p>","DOI":"10.3390\/sym15071365","type":"journal-article","created":{"date-parts":[[2023,7,6]],"date-time":"2023-07-06T00:34:30Z","timestamp":1688603670000},"page":"1365","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Generalized Fiducial Inference for the Stress\u2013Strength Reliability of Generalized Logistic Distribution"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0536-0569","authenticated-orcid":false,"given":"Menghan","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9005-7913","authenticated-orcid":false,"given":"Liang","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0049-8315","authenticated-orcid":false,"given":"Yaru","family":"Qiao","sequence":"additional","affiliation":[{"name":"School of Science, Hebei University of Science and Technology, Shijiazhuang 050018, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1512-0905","authenticated-orcid":false,"given":"Xia","family":"Cai","sequence":"additional","affiliation":[{"name":"School of Science, Hebei University of Science and Technology, Shijiazhuang 050018, China"}]},{"given":"Khamis K.","family":"Said","sequence":"additional","affiliation":[{"name":"Department of Science, Karume Institute of Science and Technology, Zanzibar P.O. Box 467, Tanzania"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,5]]},"reference":[{"key":"ref_1","unstructured":"Birnbaum, Z.W. (1954, January 26\u201331). On a use of the mann-whitney statistics. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA, USA."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1214\/aoms\/1177706631","article-title":"A distribution-free upper confidence bound for Pr(Y<X), based on independent samples of X and Y","volume":"29","author":"Birnbaum","year":"1958","journal-title":"Ann. Math. Stat."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1080\/00224065.1984.11978882","article-title":"Approximate one-sided tolerance limits for the difference or sum of two independent normal variates","volume":"16","author":"Hall","year":"1984","journal-title":"J. Qual. 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