{"title":"Estimation of P(Y<X) for lognormal distribution","authors":"Y. Tripathi, C. Petropoulos, M. Jha","doi":"10.1080/16843703.2022.2052585","DOIUrl":null,"url":null,"abstract":"ABSTRACT The problem of estimating a stress-strength parameter is considered under the assumption that both stress and strength variables follow independent lognormal distributions. The maximum likelihood estimator of this parametric function is obtained and based on its asymptotic distribution, approximate intervals are constructed. Properties of a heuristic estimator are studied as well. Bootstrap intervals are also constructed. Bayes estimator is derived against proper and improper prior distributions. We further compute credible intervals of stress–strength parameter using importance sampling. The empirical Bayes procedure is also discussed. Proposed point and interval estimators are compared numerically using Monte Carlo simulations. Analysis of a real data set is presented for illustration purposes.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"19 1","pages":"749 - 765"},"PeriodicalIF":2.3000,"publicationDate":"2022-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quality Technology and Quantitative Management","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1080/16843703.2022.2052585","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, INDUSTRIAL","Score":null,"Total":0}
引用次数: 2
Abstract
ABSTRACT The problem of estimating a stress-strength parameter is considered under the assumption that both stress and strength variables follow independent lognormal distributions. The maximum likelihood estimator of this parametric function is obtained and based on its asymptotic distribution, approximate intervals are constructed. Properties of a heuristic estimator are studied as well. Bootstrap intervals are also constructed. Bayes estimator is derived against proper and improper prior distributions. We further compute credible intervals of stress–strength parameter using importance sampling. The empirical Bayes procedure is also discussed. Proposed point and interval estimators are compared numerically using Monte Carlo simulations. Analysis of a real data set is presented for illustration purposes.
期刊介绍：
Quality Technology and Quantitative Management is an international refereed journal publishing original work in quality, reliability, queuing service systems, applied statistics (including methodology, data analysis, simulation), and their applications in business and industrial management. The journal publishes both theoretical and applied research articles using statistical methods or presenting new results, which solve or have the potential to solve real-world management problems.
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