Random Vectors from the Multivariate

The multivariate normal distribution is often the assumed distribution underlying data samples and it is widely used in pattern recognition and classiication 2]]3]]6]]7]. It is undoubtedly of great beneet to be able to generate random values and vectors from the distribution of choice given its suucient statistics or chosen parameters. We present a detailed account of the theory and algorithms involved in generating random vectors from the multivariate normal distribution given its mean vector ~ and covariance matrix using a random number generator from the univariate uniform distribution U(0; 1). 1 Road map First we introduce our notation, characterize the multivariate normal distribution and state some basic deenitions. This is followed by the relevant theory needed to understand the algorithm. Then we describe how to put it altogether to generate the random vectors. The stages are: generate n random values x 1 ; :::; x n (by separate invocations of the random number generator), where x i U(0; 1). Then x =