TT.moment: First Two Moments of Truncated Multivariate t (TMVT)...

In TTmoment: Sampling and Calculating the First and Second Moments for the Doubly Truncated Multivariate t Distribution

Description

This function calculates the first two moments of the TMVT distribution with zero location vector and correlation matrix.

Usage

TT.moment(R=diag(length(lower)), nu=5, lower=rep(-Inf, nrow(R)), upper=rep(Inf, nrow(R)))

Arguments

R	Nonsingular correlation matrix, default is diag(length(a)).
nu	Degree of freedom, must be a positive integer, nu>4 is required to calculate the second moment of TMVT distribution.
lower	Lower (left) truncation bound on the random vector, default is rep(-Inf, nrow(R)).
upper	Upper (right) truncation bound on the random vector, default is rep(Inf, nrow(R)).

Value

EX	The first moment
EXX	The second moment

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

# 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.