This paper presents a novel approach for analyzing bivariate positive data, taking into account a covariate vector and left-censored observations, by introducing a hierarchical Bayesian analysis. The proposed method assumes marginal Weibull distributions and employs either a usual Weibull likelihood or Weibull-Tobit likelihood approaches. A latent variable or frailty is included in the model to capture the possible correlation between the bivariate responses for the same sampling unit.
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