ABSTRACT
In this paper, a generalized lognormal distribution (logGN for short) is analyzed from a Bayesian viewpoint. If a random variable X has a logGNdistribution, the random variable Y = log X is distributed as a GN. The logGN distribution has the lognormal one as a particular case. Bayesian inference offers the possibility of taking expert opinions into account. This makes this approach appealing in practical problems concerning many fields of knowledge, including reliability of technical systems. The Bayesian approach is also interesting when no prior information is obtained,
in this case a noninformative prior distribution is used. The full Bayesian analysis includes a Gibbs sampling algorithm to obtain the samples from the posterior distribution of the parameters of interest. Then, the predictive distribution can be easily obtained. Empirical proofs over a wide range of engineering data sets have shown that the generalized lognormal distribution can outperform the lognormal one in this Bayesian context.
