An extension of Ryu's bivariate weibull
distribution: a bayesian application in
competing risks

Eduardo Yoshio NAKANO[1]

Josemar RODRIGUES[2]

§    abstract: The formulation of bivariate models is fundamental to explain a possible dependence between life times, since the supposition of independence in competing risks can be questionable. Some bivariate models based on the shock processes are accepted in the literature. Among them, we can mention the Marshall and Olkin’s bivariate exponential model (Marshall and Olkin, 1967) and the Ryu’s bivariate Weibull model (Ryu, 1993). In the present study, the Ryu’s bivariate model was extended to allow the shocks to change with time by modifying its suppositions. A competing risks model was formulated from this model, and using simulated data and MCMC algorithm with latent variables, its parameters were estimated via Bayesian procedures.

§    KEYWORDS: Non–identifiability; crude risk; net risk; latent variables.

[1] Departamento de Estatística, Universidade de Brasília - UnB, CEP: 70910-900, Brasília, DF, Brasil, E‑mail:

[2] Departamento de Estatística, Universidade Federal de São Carlos - UFSCar, Caixa Postal 676, CEP: 13565-905, São Carlos, SP, Brasil, E-mail: