{"title":"Estimation of the stress–strength reliability for the exponential-Rayleigh distribution","authors":"M.S. Kotb , M.A. Al Omari","doi":"10.1016/j.matcom.2024.09.005","DOIUrl":null,"url":null,"abstract":"<div><p>In this current paper, we consider the problem of estimating the stress–strength parameter <span><math><mrow><mi>ψ</mi><mo>=</mo><mi>P</mi><mrow><mo>(</mo><mi>X</mi><mo><</mo><mi>Y</mi><mo>)</mo></mrow></mrow></math></span>. This is done by using Bayesian and non-Bayesian approaches when <span><math><mi>X</mi></math></span> and <span><math><mi>Y</mi></math></span> are independent random variables from two exponential-Rayleigh distributions with different shape parameters but the same scale parameter. Maximum likelihood and Bayes estimators are used to estimate and construct the asymptotic confidence interval and credible interval of <span><math><mi>ψ</mi></math></span>. Finally, an intensive simulation study is performed to compare the proposed methods and analyze a real data set for illustrative purposes.</p></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"228 ","pages":"Pages 263-273"},"PeriodicalIF":4.4000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics and Computers in Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378475424003604","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
In this current paper, we consider the problem of estimating the stress–strength parameter . This is done by using Bayesian and non-Bayesian approaches when and are independent random variables from two exponential-Rayleigh distributions with different shape parameters but the same scale parameter. Maximum likelihood and Bayes estimators are used to estimate and construct the asymptotic confidence interval and credible interval of . Finally, an intensive simulation study is performed to compare the proposed methods and analyze a real data set for illustrative purposes.
在本文中,我们考虑了应力强度参数 ψ=P(X<Y) 的估算问题。当 X 和 Y 是来自两个指数-雷利分布的独立随机变量时,采用贝叶斯和非贝叶斯方法进行估算,这两个分布的形状参数不同,但尺度参数相同。最大似然法和贝叶斯估计法用于估计和构建 ψ 的渐近置信区间和可信区间。最后,进行了深入的模拟研究,以比较所提出的方法,并分析了一组真实数据,以作说明。
期刊介绍:
The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles.
Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO.
Topics covered by the journal include mathematical tools in:
•The foundations of systems modelling
•Numerical analysis and the development of algorithms for simulation
They also include considerations about computer hardware for simulation and about special software and compilers.
The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research.
The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.