Description Usage Arguments Value Author(s) References Examples
This function generates random variates from the truncated multivariate t (TMVT) distribution by using the slice sampling algorithm.
1 2 |
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
Hsiu J. Ho, Tsung-I Lin, Wan-Lun Wang, Aldo M. Garay, Victor H. Lachos, and Mauricio Castro
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.
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)
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