Performance of translation approach for modeling correlated non-normal variables

It is common to construct a consistent multivariate distribution from non-normal marginals and Pearson product–moment correlations using the well known translation approach. A practical variant of this approach is to match the Spearman rank correlations of the measured data, rather than the Pearson correlations. In this paper, the performance of these translation methods is evaluated based on their abilities to match the following exact solutions from one benchmark bivariate example where the joint distribution is known: (1) high order joint moments, (2) joint probability density functions (PDFs), and (3) probabilities of failure. It is not surprising to find significant errors in the joint moments and PDFs. However, it is interesting to observe that the Pearson and Spearman methods produce very similar results and neither method is consistently more accurate or more conservative than the other in terms of probabilities of failure. In addition, the maximum error in the probability of failure may not be associated with a large correlation. It can happen at an intermediate correlation.