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dc.contributor.authorGürler, Ü.en_US
dc.date.accessioned2015-07-28T11:56:08Z
dc.date.available2015-07-28T11:56:08Z
dc.date.issued1997-01en_US
dc.identifier.issn0047-259X
dc.identifier.urihttp://hdl.handle.net/11693/10870
dc.description.abstractIn random truncation models one observes the i.i.d. pairs (Ti≤Yi), i=1, ..., n. If Y is the variable of interest, then T is another independent variable which prevents the complete observation of Y and random left truncation occurs. Such a type of incomplete data is encountered in medical studies as well as in economy, astronomy, and insurance applications. Let (Y, Y) be a bivariate vector of random variables with joint distribution function F(y, x) and suppose the variable Y is randomly truncated from the left. In this study, nonparametric estimators for the bivariate distribution and hazard functions are considered. A nonparametric estimator for F(y, x) is proposed and an a.s. representation is obtained. This representation is used to establish the consistency and the weak convergence of the empirical process. An expression for the variance of the asymptotic distribution is presented and an estimator is proposed. Bivariate "diverse-hazard" vector is introduced which captures the individual and joint failure behaviors of the random variables in opposite "time" directions. Estimators for this vector are presented and the large sample properties are discussed. Possible applications and a moderate size simulation study are also presented. © 1997 Academic Press.en_US
dc.language.isoEnglishen_US
dc.source.titleJournal of Multivariate Analysisen_US
dc.relation.isversionofhttp://dx.doi.org/10.1006/jmva.1996.1630en_US
dc.subjectBivariate distributionen_US
dc.subjectBivariate diverse-hazarden_US
dc.subjectNonparametric estimationen_US
dc.subjectTruncationen_US
dc.subjectWeak convergenceen_US
dc.titleBivariate distribution and the hazard functions when a component is randomly truncateden_US
dc.typeArticleen_US
dc.departmentDepartment of Industrial Engineeringen_US
dc.citation.spage20en_US
dc.citation.epage47en_US
dc.citation.volumeNumber60en_US
dc.citation.issueNumber1en_US
dc.identifier.doi10.1006/jmva.1996.1630en_US
dc.publisherElsevieren_US


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