NORTA and neural networks based method to generate random vectors with arbitrary marginal distributions and correlation matrix

Growing technology, escalating capability, and increasing complexity in many real world systems demand the applications of multivariate statistical analysis approaches by simulation. In these approaches, generating multivariate random vectors is a crucial part of the system modeling and analyzing. The NORTA algorithm, in which generating the correlation matrices of normal random vectors is the most important task, is one of the most efficient methods in this area. To do this, we need to solve some complicated equations. Many researchers have tried to solve these equations by three general approaches of (1) solving nonlinear equations analytically, (2) solving equations numerically, and (3) solving equations by simulation. In this paper, we develop a new method to generate the correlation matrices of normal random vectors based on the artificial neural networks approach. We apply the Perseptron Neural Network as the best applicable network to function fitting. In order to understand the proposed method better, we present two numerical examples and report the results of simulation studies.