Objective Bayesian Analysis of a Generalized Lognormal Distribution

The generalized lognormal distribution plays an important role in various aspects of life testing experiments. We examine Bayesian analysis of this distribution using objective priors (in the general sense of priors constructed using some formal rules) for the model parameters in this paper. Specifically, the derivation of explicit expressions for multiple types of the Jeffreys priors, the reference priors with different group ordering of the parameters, and the first-order matching priors. We investigate the important issue of proper posterior distributions. It is shown that only two of them lead to proper posterior distributions. Monte Carlo simulations are conducted to compare the performances of the Bayesian approaches under the various priors. Last, a real-world data case will be shown to illustrate the theoretical analysis.