Draw from multivariate normal distribution

This function draws from a multivariate normal distribution.

Usage

rmvnorm(mu, Sigma)

Arguments

mu

The mean vector of length n.

Sigma

The covariance matrix of dimension n x n.

Value

A numeric vector of length n.

Details

The function builds upon the following fact: If \(\epsilon = (\epsilon_1,\dots,\epsilon_n)\), where each \(\epsilon_i\) is drawn independently from a standard normal distribution, then \(\mu+L\epsilon\) is a draw from the multivariate normal distribution \(N(\mu,\Sigma)\), where \(L\) is the lower triangular factor of the Choleski decomposition of \(\Sigma\).

Examples

mu <- c(0,0)
Sigma <- diag(2)
rmvnorm(mu = mu, Sigma = Sigma)
#>            [,1]
#> [1,] 0.04018181
#> [2,] 0.73337593