mvrnorm {MASS}  R Documentation 
Produces one or more samples from the specified multivariate normal distribution.
mvrnorm(n = 1, mu, Sigma, tol = 1e6, empirical = FALSE)
n 
the number of samples required. 
mu 
a vector giving the means of the variables. 
Sigma 
a positivedefinite symmetric matrix specifying the covariance matrix of the variables. 
tol 
tolerance (relative to largest variance) for numerical lack of
positivedefiniteness in Sigma .

empirical 
logical. If true, mu and Sigma specify the empirical not population mean and covariance matrix. 
The matrix decomposition is done via eigen
; although a Choleski
decomposition might be faster, the eigendecomposition is
stabler.
If n = 1
a vector of the same length as mu
, otherwise an
n
by length(mu)
matrix with one sample in each row.
Causes creation of the dataset .Random.seed
if it does
not already exist, otherwise its value is updated.
B. D. Ripley (1987) Stochastic Simulation. Wiley. Page 98.
Sigma < matrix(c(10,3,3,2),2,2) Sigma var(mvrnorm(n=1000, rep(0, 2), Sigma)) var(mvrnorm(n=1000, rep(0, 2), Sigma, empirical = TRUE))