# mvrnorm: Simulate from a Multivariate Normal Distribution In MASS: Support Functions and Datasets for Venables and Ripley's MASS

 mvrnorm 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`

### 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 documentation built on May 29, 2024, 8:37 a.m.