# mvrnorm

0th

Percentile

##### 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.

rnorm

• mvrnorm
##### 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 7.3-49, License: GPL-2 | GPL-3

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