# Generate random numbers from the multivariate normal distribution

### Description

`rmnorm`

generate random numbers from a multivariate normal distribution.

### Usage

1 |

### Arguments

`n` |
the number of random vectors to be generated. |

`mean` |
a vector with means of length |

`varcov` |
a variance-covariance matrix with dimentions |

### Details

This is a modification of the function `rmnorm`

provided in mnormt.
The function works around problems of non-positive definite
variance-covariance matrices due to numerical rounding by use of the
function `nearPD`

. Furthermore, when only a single random vector
is generated, the function now returns a named random vector with names
inherited from the colum names of the variance-covariance matrix.

### Value

For n > 1 `rmnorm`

returns a matrix of `n`

rows of random vectors,
while for n = 1 `rmnorm`

returns a named random vector.

### Author(s)

Fortran code of SADMVN and most auxiliary functions by Alan Genz, some additional auxiliary functions by people referred to within his program. Porting to R and additional R code by Adelchi Azzalini, with current modifications by Thomas Kvalnes.

### References

Genz, A. 1992. Numerical Computation of Multivariate Normal Probabilities. Journal of Computational and Graphical Statiststics, 1, 141-149.

Genz, A. 1993. Comparison of methods for the computation of multivariate normal probabilities. Computing Science and Statistics, 25, 400-405.

Genz, A.: Fortran code available at http://www.math.wsu.edu/math/faculty/genz/software/fort77/mvn.f

### See Also

`Normal`

, `rnorm`

, `rmnorm`

,
`nearPD`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ```
#Variance-covariance matrix
varcov <- matrix(c(2.047737e-03, 3.540039e-05, 0.0075178920, 3.540039e-05,
6.122832e-07, 0.0001299661, 7.517892e-03, 1.299661e-04, 0.0276005740), ncol = 3)
#Set names
nam <- c("a", "b", "c")
dimnames(varcov) <- list(nam, nam)
#Check positive definiteness (all positive eigenvalues = positive definite)
eigen(varcov) $values
#Mean
mean <- c(1, 0.3, 0.5)
#Generate n = 1 random vector
rmnorm(n = 1, mean = mean, varcov = varcov)
#Generate n = 10 random vectors
rmnorm(n = 10, mean = mean, varcov = varcov)
#Generate n = 1 random vectors when varcov is non-positive definite
#Non-positive definite varcov matrix
varcov2 <- matrix(c(2.04e-03, 3.54e-05, 7.52e-03, 3.54e-05, 6.15e-07,
1.30e-04, 7.52e-03, 1.30e-04, 2.76e-02), ncol = 3)
dimnames(varcov2) <- dimnames(varcov)
eigen(varcov2)
#Random vector
rmnorm(n = 1, mean = mean, varcov = varcov2)
``` |