rmvn {mgcv} | R Documentation |

## Generate from or evaluate multivariate normal or t densities.

### Description

Generates multivariate normal or t random deviates, and evaluates the corresponding log densities.

### Usage

```
rmvn(n,mu,V)
r.mvt(n,mu,V,df)
dmvn(x,mu,V,R=NULL)
d.mvt(x,mu,V,df,R=NULL)
```

### Arguments

`n` |
number of simulated vectors required. |

`mu` |
the mean of the vectors: either a single vector of length |

`V` |
A positive semi definite covariance matrix. |

`df` |
The degrees of freedom for a t distribution. |

`x` |
A vector or matrix to evaluate the log density of. |

`R` |
An optional Cholesky factor of V (not pivoted). |

### Details

Uses a ‘square root’ of `V`

to transform standard normal deviates to multivariate normal with the correct covariance matrix.

### Value

An `n`

row matrix, with each row being a draw from a multivariate normal or t density with covariance matrix `V`

and mean vector `mu`

. Alternatively each row may have a different mean vector if `mu`

is a vector.

For density functions, a vector of log densities.

### Author(s)

Simon N. Wood simon.wood@r-project.org

### See Also

### Examples

```
library(mgcv)
V <- matrix(c(2,1,1,2),2,2)
mu <- c(1,3)
n <- 1000
z <- rmvn(n,mu,V)
crossprod(sweep(z,2,colMeans(z)))/n ## observed covariance matrix
colMeans(z) ## observed mu
dmvn(z,mu,V)
```

*mgcv*version 1.9-0 Index]