Posterior propriety of bivariate lomax distribution under objective priors

The Lomax or Pareto II, distribution has been quite widely used for reliability modeling and life testing, and applied to the sizes of computer files on servers, and even application in the biological sciences. Especially, the bivariate Lomax distribution is considered for a two components system which works under interdependency circumstances. We here develop the noninformative priors such as the probability matching priors and the reference priors for the parameters in the bivariate lomax population. It turns out that the reference prior satisfy a first order matching criterion only for some parameter groupings. We also check the conditions for the propriety of posterior distributions under the general prior class including the matching priors and the reference priors. It is a quite interesting that the posterior distributions under the reference priors for some parameter groupings are proper, but those for the other parameter groupings are improper. However all of the matching priors give the proper posteriors.