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The Bivariate Kumaraswamy Weibull regression model: a complete classical and Bayesian analysis
Commun. Stat. Appl. Methods, CSAM 2018;25:523-544
Published online September 30, 2018
© 2018 Korean Statistical Society.

Juliana B. Fachini-Gomesa, Edwin M. M. Ortegab, Gauss M. Cordeiroc, Adriano K. Suzuki1,d

aDepartment of Statistics, University of Brasilia, Brazil;
bDepartment of Exact Sciences, University of São Paulo, Brazil;
cDepartment of Statistics, Federal University of Pernambuco, Brazil;
dDepartment of Applied Mathematics and Statistics, University of São Paulo, Brazil
Correspondence to: Department of Applied Mathematics and Statistics, University of São Paulo, Avenida Trabalhador São-carlense, 400 - Centro CEP: 13566-590, São Carlos-SP, Brazil. E-mail: suzuki@icmc.usp.br
Received March 20, 2018; Revised June 23, 2018; Accepted August 14, 2018.
 Abstract
Bivariate distributions play a fundamental role in survival and reliability studies. We consider a regression model for bivariate survival times under right-censored based on the bivariate Kumaraswamy Weibull (Cordeiro et al., Journal of the Franklin Institute, 347, 1399–1429, 2010) distribution to model the dependence of bivariate survival data. We describe some structural properties of the marginal distributions. The method of maximum likelihood and a Bayesian procedure are adopted to estimate the model parameters. We use diagnostic measures based on the local influence and Bayesian case influence diagnostics to detect influential observations in the new model. We also show that the estimates in the bivariate Kumaraswamy Weibull regression model are robust to deal with the presence of outliers in the data. In addition, we use some measures of goodness-of-fit to evaluate the bivariate Kumaraswamy Weibull regression model. The methodology is illustrated by means of a real lifetime data set for kidney patients.
Keywords : Bayesian inference, bivariate failure time, censored data, diagnostics, survival analysis