# TT.GS: Slice Sampling for the Truncated Multivariate t (TMVT)... In TTmoment: Sampling and Calculating the First and Second Moments for the Doubly Truncated Multivariate t Distribution

## Description

This function generates random variates from the truncated multivariate t (TMVT) distribution by using the slice sampling algorithm.

## Usage

 ```1 2``` ```TT.GS(n, mu=rep(0,nrow(S)), S=diag(length(mu)), nu=2, lower=rep(-Inf, length(mu)), upper=rep(Inf, length(mu))) ```

## Arguments

 `n` Number of observations. `mu` Location vector, default is rep(0, length = nrow(S)). `S` Scale matrix, default is diag(length(mu)). `nu` Degree of freedom, nu>2 is required to confirm the existence of the first two moments of TMVT distribution under slice sampling. `lower, upper` Truncation bounds on the random vectors, default is rep(-Inf, length(mu)), rep(Inf, length(mu)).

An n by p matrix

## Author(s)

Hsiu J. Ho, Tsung-I Lin, Wan-Lun Wang, Aldo M. Garay, Victor H. Lachos, and Mauricio Castro

## References

Hsiu J. Ho, Tsung-I Lin, Hsuan-Yu Chen, Wan-Lun Wang (2012), Some results on the truncated multivariate t distribution. Journal of Statistical Planning and Inference, 142, 25-40.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```# A test example rho=0.9 S=matrix(c(1, rho ,rho, 1),2,2) nu=5 p=2 mu = rep(0, p) Y= TT.GS(n=10000, mu, S, nu, lower=c(1,2), upper=c(4,6)) # Empirical first moment y.bar=colMeans(Y) y.bar # Sample covariance matrix S.y=cov(Y) S.y M.Y=TT.moment(R=S, nu, lower=c(1,2), upper=c(4,6)) # First two moments M.Y\$EX M.Y\$EXX # Covariance matrix M.Y\$EXX-M.Y\$EX%*%t(M.Y\$EX) ```

TTmoment documentation built on May 1, 2019, 7:50 p.m.