First and foremost, I really appreciate your detailed reply. In particular, your discussion about the “Rare Event Estimation”. Is there any chance for me to have your guidance on the below questions?
1- As you are well aware, choosing some specific marginal could help us to capture the “tail dependency”. Assume a hypothetical situation in which UQLab proposes a lognormal distribution (based on his GOF tests). The challenge begins here:
Is it possible to use marginals such as Gumbel to investigate the tail dependency which shows worse AIC or BIC than the proposed UQLab lognormal distribution to show tail dependency?
In a sentence, could our purpose overwhelm the GOF tests to show the tail dependency?
2- In the context of nonparametric marginal, consider UQLab suggests one parametric distribution (e.g Logistic) which shows good GOF, if I use the “nonparametric inference marginal” option in UQLab (iOpts.Marginals(i).Type = ‘ks’ ), Does the probability of failure (Pf) which comes from the nonparametric approach show reliable results (Pf) or not?
In other words, if I use two different approaches (i.e., parametric and nonparametric) and face two different results (Pf) from the reliability analysis which one is correct?
(Assume the parametric inference marginal approach satisfies the GOF tests)
Last but not least, thanks for your enjoyable and state of the art platform, UQLab.