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

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

the number of samples required.

a vector giving the means of the variables.

a positive-definite symmetric matrix specifying the covariance matrix of the variables.

tolerance (relative to largest variance) for numerical lack of positive-definiteness in Sigma.

Sigma

logical. If true, mu and Sigma specify the empirical not population mean and covariance matrix.

logical: values other than FALSE are an error.

FALSE

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

n = 1

mu

n

length(mu)

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

.Random.seed

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

eigen

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

rnorm

# NOT RUN { 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)) # }

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