Generate from or evaluate multivariate normal or t densities.

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

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 p=ncol(V) or an n by p matrix.

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).

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.

Details

Uses a `square root' of V to transform standard normal deviates to multivariate normal with the correct covariance matrix.

Author

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

See also

ldTweedie, Tweedie

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
#>          [,1]     [,2]
#> [1,] 1.959609 1.012001
#> [2,] 1.012001 2.108240
colMeans(z) ## observed mu
#> [1] 0.9734437 3.0243813
dmvn(z,mu,V)
#> [1] -2.506170 -5.631153