mvrnorm {MASS} R Documentation

## 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 = FALSE, EISPACK = FALSE)


### Arguments

 n the number of samples required. 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. EISPACK logical: values other than FALSE are an error.

### Details

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

### 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.

### References

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

rnorm
Sigma <- matrix(c(10,3,3,2),2,2)