# mvrnorm

From MASS v7.3-16
by Brian Ripley

##### 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)`

##### 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.

##### 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

```
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 7.3-16, License: GPL-2 | GPL-3*

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