R: Multivariate Normal Density and Random Deviates

Mvnorm {mvtnorm}

R Documentation

Multivariate Normal Density and Random Deviates

Description

These functions provide the density function and a random number generator for the multivariate normal distribution with mean equal to mean and covariance matrix sigma.

Usage

dmvnorm(x, mean, sigma, log=FALSE)
rmvnorm(n, mean = rep(0, nrow(sigma)), sigma = diag(length(mean)),
        method=c("eigen", "svd", "chol"))

Arguments

`x`	Vector or matrix of quantiles. If `x` is a matrix, each row is taken to be a quantile.
`n`	Number of observations.
`mean`	Mean vector, default is `rep(0, length = ncol(x))`.
`sigma`	Covariance matrix, default is `diag(ncol(x))`.
`log`	Logical; if `TRUE`, densities d are given as log(d).
`method`	Matrix decomposition used to determine the matrix root of `sigma`, possible methods are eigenvalue decomposition (`"eigen"`, default), singular value decomposition (`"svd"`), and Cholesky decomposition (`"chol"`).

Author(s)

Friedrich Leisch and Fabian Scheipl

Examples

dmvnorm(x=c(0,0))
dmvnorm(x=c(0,0), mean=c(1,1))

sigma <- matrix(c(4,2,2,3), ncol=2)
x <- rmvnorm(n=500, mean=c(1,2), sigma=sigma)
colMeans(x)
var(x)

x <- rmvnorm(n=500, mean=c(1,2), sigma=sigma, method="chol")
colMeans(x)
var(x)

plot(x)