Objective Bayesian inference for the reliability in a bivariate Lomax distribution

We consider the objective Bayesian analysis for the reliability in the bivariate Lomax distribution. In this paper, we derive the first- and second-order matching priors and the reference priors for the reliability in the bivariate Lomax population. However, it turns out that the reference priors do not satisfy the first-order matching criterion and also, the matching priors and the reference priors have different distributions. We provide conditions for the general prior, including the matching and reference priors, to generate proper posterior distributions. Our simulation shows that the matching prior matches the target coverage probabilities well in a frequentist sense. Furthermore, even when the reference priors do not satisfy the first-order matching criterion, they still perform as well as the second-order matching prior. Finally, we demonstrate our results using two real examples.