# mvrnorm

##### Simulate from a Multivariate Normal Distribution

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

- Keywords
- multivariate, 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.

##### See Also

##### Examples

```
# 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))
# }
```

*Documentation reproduced from package MASS, version 7.3-51.1, License: GPL-2 | GPL-3*