Predictive discrepancy of credible intervals for the parameter of the Rayleigh distribution

The two most commonly used methods for Bayesian set estimation of an unknown one-dimensional parameter are equal-tails and highest posterior density intervals. The resulting estimates may be numerically different for specific observed samples but they tend to become closer and closer as the sample size increases. In this article we consider a pre-posterior measure of the progressive overlap between these two types of intervals and relationships with the skewness of the posterior distribution. We illustrate the implementation of the method for the Rayleigh model that is often used in the context of reliability and survival analysis.