# Mvnorm

##### Multivariate Normal Density and Random Deviates

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`

.

- Keywords
- multivariate, distribution

##### Usage

```
dmvnorm(x, mean = rep(0, p), sigma = diag(p), log = FALSE, checkSymmetry = TRUE)
rmvnorm(n, mean = rep(0, nrow(sigma)), sigma = diag(length(mean)),
method=c("eigen", "svd", "chol"), pre0.9_9994 = FALSE, checkSymmetry = TRUE)
```

##### 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
string specifying the 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"`

). The Cholesky is typically fastest, not by much though.- pre0.9_9994
logical; if

`FALSE`

, the output produced in mvtnorm versions up to 0.9-9993 is reproduced. In 0.9-9994, the output is organized such that`rmvnorm(10,...)`

has the same first ten rows as`rmvnorm(100, ...)`

when called with the same seed.- checkSymmetry
logical; if

`FALSE`

, skip checking whether the covariance matrix is symmetric or not. This will speed up the computation but may cause unexpected outputs when ill-behaved`sigma`

is provided. The default value is`TRUE`

.

##### See Also

##### Examples

```
# NOT RUN {
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)
# }
```

*Documentation reproduced from package mvtnorm, version 1.1-1, License: GPL-2*