MultiRNG (version 1.2.4)

draw.d.variate.t: Pseudo-Random Number Generation under Multivariate t Distribution

Description

This function implements pseudo-random number generation for a multivariate \(t\) distribution with pdf

$$f(x|\mu, \Sigma, \nu)=c\left(1+\frac{1}{\nu}(x-\mu)^{T}\Sigma^{-1}(x-\mu)\right)^{-(\nu+d)/2}$$

for \(-\infty < x < \infty\) and \(c=\frac{\Gamma((\nu+d)/2)}{\Gamma(\nu/2)(\nu\pi)^{d/2}}|\Sigma|^{-1/2}\), \(\Sigma\) is symmetric and positive definite, \(\nu>0\), where \(\mu\), \(\Sigma\), and \(\nu\) are the mean vector, the variance-covariance matrix, and the degrees of freedom, respectively.

Usage

draw.d.variate.t(dof,no.row,d,mean.vec,cov.mat)

Arguments

dof

Degrees of freedom.

no.row

Number of rows to generate.

d

Number of variables to generate.

mean.vec

Vector of means.

cov.mat

Variance-covariance matrix.

Value

A \(no.row \times d\) matrix of generated data.

Examples

# NOT RUN {
cmat<-matrix(c(1,0.2,0.3,0.2,1,0.2,0.3,0.2,1), nrow=3, ncol=3)
meanvec=c(0,3,7)
mydata=draw.d.variate.t(dof=5,no.row=1e5,d=3,mean.vec=meanvec,cov.mat=cmat)
apply(mydata,2,mean)-meanvec
cor(mydata)-cmat
# }