Posterior properties under matching priors for generalized gamma distribution

Recently, the overall reference prior has been proposed for parameters of the generalized gamma distribution. As an alternative, here we develop a matching prior that provides the same coverage probability asymptotically as a Bayesian credible interval with the corresponding frequentist counterpart, and subsequently show that this matching prior yields proper posteriors. In addition, we find that the overall reference prior is not a first-order matching prior. Simulation studies show that the derived matching priors perform better than the overall reference prior in meeting the target coverage probabilities, and meets the target coverage probabilities well even for a small sample size.