{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:34:34Z","timestamp":1760240074033,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,3,7]],"date-time":"2019-03-07T00:00:00Z","timestamp":1551916800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Nos. 50678143 and 51278401"],"award-info":[{"award-number":["Nos. 50678143 and 51278401"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In engineering practice, it is sometimes necessary to infer the representative value of variable action under the condition that the test data is insufficient, but the classical statistics methods adopted now do not take into account the influences of statistical uncertainty, and the inferring results are always small, especially when characteristic and frequent values are inferred. Variable actions usually obey a type I maximum distribution, so the linear regression estimation of the tantile of type I minimum distribution can be employed to infer their characteristic and frequent values. However, it is inconvenient to apply and cannot totally meet the demands of characteristic and frequent values inference. Applying Jeffreys non-informative prior distribution, Bayesian methods for inferring characteristic and frequent values of variable actions are put forward, including that with known standard deviation, which could yield more advantageous results. The methods proposed are convenient and flexible, possessing good precision.<\/jats:p>","DOI":"10.3390\/sym11030346","type":"journal-article","created":{"date-parts":[[2019,3,8]],"date-time":"2019-03-08T04:58:35Z","timestamp":1552021115000},"page":"346","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Bayesian Methods of Representative Values of Variable Actions"],"prefix":"10.3390","volume":"11","author":[{"given":"Xudong","family":"Wang","sequence":"first","affiliation":[{"name":"School of Science, Xi\u2019an University of Architecture and Technology, Xi\u2019an 710055, China"}]},{"given":"Jitao","family":"Yao","sequence":"additional","affiliation":[{"name":"School of Science, Xi\u2019an University of Architecture and Technology, Xi\u2019an 710055, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,7]]},"reference":[{"key":"ref_1","unstructured":"National Standard of the People\u2019s Republic of China (2009). Unified Standard for Reliability Design of Engineering Structures (GB50153-2008), China Architecture and Building Press."},{"key":"ref_2","first-page":"307","article-title":"Statistical inference of material strength of existing structures","volume":"35","author":"Yao","year":"2003","journal-title":"J. Xi\u2019an Univ. Archit. Technol."},{"key":"ref_3","first-page":"74","article-title":"Determination of frequent value and quasi-permanent value of floor live load and wind load","volume":"42","author":"Feng","year":"2012","journal-title":"Ind. Constr."},{"key":"ref_4","unstructured":"National Standard of the People\u2019s Republic of China (1984). Unified Standard for Design of Building Structures (GBJ68-84), China Architecture and Building Press."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1007\/s10255-013-0222-6","article-title":"Bayesian Estimation for Generalized Exponential Distribution Based on Progressive Type-I Interval Censoring","volume":"29","author":"Peng","year":"2013","journal-title":"Acta Math. Appl. Sin."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1811","DOI":"10.1080\/02664763.2012.683170","article-title":"Bayesian inference under progressive type-I interval censoring","volume":"39","author":"Lin","year":"2012","journal-title":"J. Appl. Stat."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.jspi.2008.05.016","article-title":"Planning life tests with progressively Type-I interval censored data from the lognormal distribution","volume":"139","author":"Lin","year":"2009","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1002\/1521-4036(200102)43:1<117::AID-BIMJ117>3.0.CO;2-R","article-title":"Exponentiated exponential family: An alternative to Gamma and Weibull distributions","volume":"43","author":"Gupta","year":"2001","journal-title":"Biom. J."},{"key":"ref_9","unstructured":"Mao, S.S. (2003). Statistics Handbook, Beijing Science Press."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1921","DOI":"10.1081\/STA-100105705","article-title":"Interval censoring: Some mathematical results application to inference","volume":"30","author":"Aggarwala","year":"2001","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_11","unstructured":"Zhou, Y.Q. (1997). The Quality of Reliability Growth and Reliability Evaluation Method, Beihang University Press."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1373","DOI":"10.1007\/s11425-009-0085-8","article-title":"Bayesian inference and life testing plans for generalized exponential distribution","volume":"52","author":"Kundu","year":"2009","journal-title":"Sci. China Ser. A Math."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1023\/B:STCO.0000035302.87186.be","article-title":"Bayesian inference for multivariate gamma distributions","volume":"14","author":"Efthymios","year":"2004","journal-title":"Stat. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/s00362-009-0197-9","article-title":"Estimation of the scale parameter of the half-logistic distribution under progressively type II censored sample","volume":"51","author":"Chansoo","year":"2010","journal-title":"Stat. Pap."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1007\/s11222-011-9257-9","article-title":"Free energy methods for Bayesian inference: Efficient exploration of univariate Gaussian mixture posteriors","volume":"22","author":"Chopin","year":"2012","journal-title":"Stat. Comput."},{"key":"ref_16","unstructured":"Research Department of Machinery Industry Standard Fourth (1979). Table for Reliability Test, National Defence Industry Press."},{"key":"ref_17","unstructured":"Dai, S.S., and Fei, H.L. (1983). Reliability Test and Statistical Analysis (First Book), National Defence Industry Press."},{"key":"ref_18","unstructured":"Mao, S.S. (1999). Bayes Statistics, China Statistics Press."},{"key":"ref_19","unstructured":"Yao, J.T. (2001). Reliability Assessment of Existing Structure Based on Uncertainty Reasoning Theory, Science Press."},{"key":"ref_20","unstructured":"National Standard of the People\u2019s Republic of China (2001). Load Code for the Design of Building Structures (GB50009-2001), China Architecture and Building Press."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"23","DOI":"10.20937\/RICA.2017.33.esp02.02","article-title":"Air quality regarding metals (pb, cd, ni, cu, cr) and relationship with respiratory health: Caso sonora, mexico","volume":"33","year":"2017","journal-title":"Rev. Int. Contam. Ambient."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1039\/C7FO00835J","article-title":"Molecular actions of hypocholesterolaemic compounds from edible mushrooms","volume":"9","author":"Morales","year":"2018","journal-title":"Food Funct."},{"key":"ref_23","first-page":"47","article-title":"The risk management of perishable supply chain based on coloured petri net modeling","volume":"5","author":"Liu","year":"2018","journal-title":"Inf. Process. Agric."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1080\/15567249.2017.1416704","article-title":"What is the future of solar energy? Economic and policy barriers","volume":"13","author":"Liu","year":"2018","journal-title":"Energy Sources Part B Econ. Plan. Policy"},{"key":"ref_25","first-page":"107","article-title":"Impact of production season on the chemical composition and health properties of goat milk and rennet cheese","volume":"30","author":"Milewski","year":"2018","journal-title":"Emir. Emir. J. Food Agric."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1016\/j.sjbs.2017.08.010","article-title":"Properties of antibacterial bioboard from bamboo macromolecule by hot press","volume":"25","author":"Wang","year":"2018","journal-title":"Saudi J. Biol. 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