Generation of Correlated Non-gaussian Random Variables from Independent Components

Simulations are often needed when the performance of new methods is evaluated. If the method is designed to be blind or robust, simulation studies must cover the whole range of potential random input. It follows that there is a need for advanced tools of data generation. The purpose of this paper is to introduce a technique for the generation of correlated multivariate random data with non-Gaussian marginal distributions. The output random variables are obtained as linear combinations of independent components. The covariance matrix and the first four moments of the output variables may be freely chosen. Moreover, the output variables may be filtered in order to add autocorrelation. Extended Generalized Lambda Distribution (EGLD) is proposed as a distribution for the independent components. Examples demonstrate the diversity of data structures that can be generated.