Two methods of conjoint summands of generating bivariate and trivariate normal pseudo-random numbers

Abstract

The primary aim of the paper is to put forward methods of generating two dimensional (2D) and three dimensional (3D) normal pseudo-random numbers (NPRNs). Both proposed methods are presented in two versions. The first version is based on uniform (0,1) random variables, while the second version is based on normal random variables. Joint summands in these methods make resulting normal numbers correlated. The secondary aim of the paper is to compare the existing methods of generating 2D and 3D NPRNs with new proposals using goodness-of-fit tests (GoFTs), generation time and specially defined measures. The obtained results indicate that the methods based on uniform (0,1) random variables are faster than the others (have the best computational complexity) and also stand out from the other measures and GoFTs used.