rmvnorm {dae} | R Documentation |

## generates a vector of random values from a multivariate normal distribution

### Description

Generates a vector of random values from an n-dimensional
multivariate normal distribution whose mean is given by the
n-vector `mean`

and variance by the
n x n symmetric matrix `V`

. It uses the method described by
Ripley (1987, p.98)

### Usage

`rmvnorm(mean, V, method = 'eigenanalysis')`

### Arguments

`mean` |
The mean vector of the multivariate normal distribution from which the random values are to be generated. |

`V` |
The variance matrix of the multivariate normal distribution from which the random values are to be generated. |

`method` |
The method used to decompose the variance matrix in producing a
a matrix to transform the iid standard normal values. The two
methods available are |

### Details

The method is:
a) uses either the eigenvalue or Choleski decomposition of the variance matrix,
`V`

, to form the matrix that transforms an iid vector of values to a
vector with variance `V`

;
b) generate a vector of length equal to `mean`

of standard normal values;
c) premultiply the vector of standard normal values by the transpose of the
upper triangular factor and, to the result, add `mean`

.

### Value

A `vector`

of length n, equal to the length of `mean`

.

### Author(s)

Chris Brien

### References

Ripley, B. D. (1987) *Stochastic simulation*. Wiley, New York.

### See Also

`fac.ar1mat`

, `fac.vcmat`

,
in package dae, `rnorm`

, and `chol`

.

### Examples

```
## set up a two-level factor and a three-level factor, both of length 12
A <- factor(rep(1:2, each=6))
B <- factor(rep(1:3, each=2, times=2))
## generate random values from a multivariate normal for which
#the mean is 20 for all variables and
#the variance matrix has random effects for factor A, ar1 pattern for B and
#residual random variation
mean <- rep(20, 12)
V <- fac.vcmat(A, 5) + fac.ar1mat(B, 0.6) + 2*mat.I(12)
y <- rmvnorm(mean, V)
```

*dae*version 3.2.28 Index]