{"title":"一些二元相关Beta分布和Kumaraswamy分布的信度综述","authors":"I. Ghosh","doi":"10.1515/eqc-2018-0029","DOIUrl":null,"url":null,"abstract":"Abstract In the area of stress-strength models, there has been a large amount of work regarding the estimation of the reliability R = Pr ( X < Y ) {R=\\Pr(X<Y)} . The algebraic form for R = Pr ( X < Y ) {R=\\Pr(X<Y)} has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same univariate family. In this paper, forms of R are considered when ( X , Y ) {(X,Y)} follow bivariate distributions with dependence between X and Y. In particular, explicit expressions for R are derived when the joint distribution are dependent bivariate beta and bivariate Kumaraswamy. The calculations involve the use of special functions.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"11 1","pages":"115 - 121"},"PeriodicalIF":0.0000,"publicationDate":"2019-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"On the Reliability for Some Bivariate Dependent Beta and Kumaraswamy Distributions: A Brief Survey\",\"authors\":\"I. Ghosh\",\"doi\":\"10.1515/eqc-2018-0029\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In the area of stress-strength models, there has been a large amount of work regarding the estimation of the reliability R = Pr ( X < Y ) {R=\\\\Pr(X<Y)} . The algebraic form for R = Pr ( X < Y ) {R=\\\\Pr(X<Y)} has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same univariate family. In this paper, forms of R are considered when ( X , Y ) {(X,Y)} follow bivariate distributions with dependence between X and Y. In particular, explicit expressions for R are derived when the joint distribution are dependent bivariate beta and bivariate Kumaraswamy. The calculations involve the use of special functions.\",\"PeriodicalId\":37499,\"journal\":{\"name\":\"Stochastics and Quality Control\",\"volume\":\"11 1\",\"pages\":\"115 - 121\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-03-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Stochastics and Quality Control\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/eqc-2018-0029\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastics and Quality Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/eqc-2018-0029","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
On the Reliability for Some Bivariate Dependent Beta and Kumaraswamy Distributions: A Brief Survey
Abstract In the area of stress-strength models, there has been a large amount of work regarding the estimation of the reliability R = Pr ( X < Y ) {R=\Pr(X
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