draw.d.variate.t {MultiRNG}

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

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