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 |

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

`EISPACK` |
logical: values other than |

### 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))
```

*MASS*version 7.3-61 Index]