Simulate from a Multivariate Normal Distribution

DESCRIPTION:

Produces one or more samples from the specified multivariate normal distribution.

USAGE:

mvrnorm(n = 1, mu, Sigma, tol = 1e-6, empirical = F)

REQUIRED ARGUMENTS:

n
the number of samples required.

OPTIONAL ARGUMENTS:

mu
a vector giving the means of the variables.
Sigma
a positive-definite symmetric matrix specifying the covariance matrix of the variables.
tol
tolerance (relative to largest variance) for numerical lack of positive-definiteness in Sigma.
empirical
logical. If true, mu and Sigma specify the empirical not population mean and covariance matrix.

VALUE:

If n = 1 a vector of the same length as mu , otherwise an n by length(mu) matrix with one sample in each row.

SIDE EFFECTS:

Causes creation of the dataset .Random.seed if it does not already exist, otherwise its value is updated.

DETAILS:

The matrix decomposition is done via eigen ; although a Choleski decomposition might be faster, the eigendecomposition is stabler.

REFERENCE:

B. D. Ripley (1987) Stochastic Simulation. Wiley. Page 98.

SEE ALSO:

, .

EXAMPLES:

Sigma <- matrix(c(10,3,3,2), 2, 2)
Sigma
var(mvrnorm(n = 1000, rep(0, 2), Sigma))