Abstract
Based on limited amount of multivariate soil data (Y) under bar, it is only possible to reliably estimate the marginal distributions and the correlations. A common practical approach of constructing the multivariate probability distribution of (Y) under bar is to transform (Y) under bar into standard normal data (X) under bar and construct the multivariate standard normal distribution for (X) under bar. This method is called the translation method. Its success depends on whether the Pearson product-moment correlations (delta(ij)) for (X) under bar can be robustly estimated. This paper investigates the robustness for four methods of estimating delta(ij). The emphasis is on the statistical uncertainty in the estimated delta(ij) when the amount of soil data is limited. It is found that the well known method that maps the Pearson correlations for (Y) under bar to delta(ij) is the least robust, suffering the most significant statistical uncertainty. The causes for this non-robustness are investigated. The two methods that map the Spearman and Kendall rank correlations for (Y) under bar to delta(ij) are quite robust. The method that converts (Y) under bar to (X) under bar and directly estimates delta(ij) is also robust as long as the conversion is based on properly chosen marginal distributions. (C) 2016 Elsevier Ltd. All rights reserved.