# rmvnorm: Generate Random Samples from Multivariate Normal Distribution In Riemann: Learning with Data on Riemannian Manifolds

 rmvnorm R Documentation

## Generate Random Samples from Multivariate Normal Distribution

### Description

In \mathbf{R}^p, random samples are drawn

X_1,X_2,…,X_n~ \sim ~ \mathcal{N}(μ, Σ)

where μ \in \mathbf{R}^p is a mean vector and Σ \in \textrm{SPD}(p) is a positive definite covariance matrix.

### Usage

rmvnorm(n = 1, mu, sigma)


### Arguments

 n the number of samples to be generated. mu mean vector. sigma covariance matrix.

### Value

either (1) a length-p vector (n=1) or (2) an (n\times p) matrix where rows are random samples.

### Examples

#-------------------------------------------------------------------
#   Generate Random Data and Compare with Empirical Covariances
#
# In R^5 with zero mean and diagonal covariance,
# generate 100 and 200 observations and compute MLE covariance.
#-------------------------------------------------------------------
## GENERATE DATA
mymu  = rep(0,5)
mysig = diag(5)

## MLE FOR COVARIANCE
smat1 = stats::cov(rmvnorm(n=100, mymu, mysig))
smat2 = stats::cov(rmvnorm(n=200, mymu, mysig))

## VISUALIZE