Multivariate extension to the exponentiated weibull distribution with analysis of confidence regions

In many situations, it is of interest to construct a parametric model for a collection of dependent random variables that are not necessarily Gaussian. Methods of constructing multivariate models using both a one-to-one transformation and copulas are given. With these constructions, methods of sampling and inference are discussed. These methods are applied to a particular multivariate extension of the exponentiated Weibull distribution, where there is discussion of the adequacy of these procedures using empirical measures.