Improving extremal fit: a Bayesian regularization procedure

In structural reliability, special attention is devoted to model distribution tails. The distributions are required to fit the upper observations and provide a picture of the tail above the maximal observation. Goodness-of-fit tests can be constructed to check this tail fit. Then what can we do with distributions having a good central fit and a bad extremal fit? We propose a regularization procedure. It is based on Bayesian tools and takes into account the opinion of experts. Predictive distributions are proposed as model distributions. We numerically investigate this method on normal, lognormal, exponential, gamma and Weibull distributions.