Bayesian analysis of a generalized lognormal distribution

Many data arising in reliability engineering can be modeled by a lognormal distribution. Empirical evidences from many sources support this argument. However, sometimes the lognormal distribution does not completely satisfy the fitting expectations in real situations. This fact motivates the use of a more flexible family of distributions with both heavier and lighter tails compared to the lognormal one, which is always an advantage for robustness. A generalized form of the lognormal distribution is presented and analyzed from a Bayesian viewpoint. By using a mixture representation, inferences are performed via Gibbs sampling. Although the interest is focused on the analysis of lifetime data coming from engineering studies, the developed methodology is potentially applicable to many other contexts. A simulated and a real data set are presented to illustrate the applicability of the proposed approach.