MomTrunc (version 4.59)

meanvarTMD: Mean and variance for doubly truncated multivariate distributions

Description

It computes the mean vector and variance-covariance matrix for the doubly truncated p-variate Normal, Skew-normal (SN), Extended Skew-normal (ESN) and Student's t-distribution.

Usage

meanvarTMD(lower = NULL,upper = NULL,mu,Sigma,lambda = NULL,tau = NULL,dist,nu = NULL)

Arguments

lower

the vector of lower limits of length \(p\).

upper

the vector of upper limits of length \(p\).

mu

a numeric vector of length \(p\) representing the location parameter.

Sigma

a numeric positive definite matrix with dimension \(p\)x\(p\) representing the scale parameter.

lambda

a numeric vector of length \(p\) representing the skewness parameter for SN and ESN cases. If lambda == 0, the ESN/SN reduces to a normal (symmetric) distribution.

tau

It represents the extension parameter for the ESN distribution. If tau == 0, the ESN reduces to a SN distribution.

dist

represents the folded distribution to be computed. The values are normal, SN , ESN and t for the doubly truncated Normal, Skew-normal, Extended Skew-normal and Student's t-distribution respectively.

nu

It represents the degrees of freedom for the Student's t-distribution.

Value

It returns a list with three elements:

mean

the mean vector of length \(p\)

EYY

the second moment matrix of dimensions \(p\)x\(p\)

varcov

the variance-covariance matrix of dimensions \(p\)x\(p\)

Warning

The mean can only be provided when nu is larger than 2. By the other hand, the varcov matrix can only be provided when nu is larger than 3.

Details

Univariate case is also considered, where Sigma will be the variance \(\sigma^2\). Normal case code is an R adaptation of the Matlab available function dtmvnmom.m from Kan & Robotti (2017) and it is used for p<=3. For higher dimensions we use an extension of the algorithm in Vaida (2009).

References

Kan R. & Robotti C. (2017) On Moments of Folded and Truncated Multivariate Normal Distributions, Journal of Computational and Graphical Statistics, 26:4, 930-934.

C.E. Galarza, L.A. Matos, D.K. Dey & V.H. Lachos. (2019) On Moments of Folded and Truncated Multivariate Extended Skew-Normal Distributions. Technical report. ID 19-14. University of Connecticut.

Vaida, F. & Liu, L. (2009). Fast implementation for normal mixed effects models with censored response. Journal of Computational and Graphical Statistics, 18(4), 797-817.

See Also

momentsTMD, meanvarFMD, meanvarFMD, momentsFMD,dmvESN,rmvESN

Examples

# NOT RUN {
a = c(-0.8,-0.7,-0.6)
b = c(0.5,0.6,0.7)
mu = c(0.1,0.2,0.3)
Sigma = matrix(data = c(1,0.2,0.3,0.2,1,0.4,0.3,0.4,1),
               nrow = length(mu),ncol = length(mu),byrow = TRUE)
value1 = meanvarTMD(a,b,mu,Sigma,dist="normal")
value2 = meanvarTMD(a,b,mu,Sigma,dist = "t",nu = 4)
value3 = meanvarTMD(a,b,mu,Sigma,lambda = c(-2,0,1),dist = "SN")
value4 = meanvarTMD(a,b,mu,Sigma,lambda = c(-2,0,1),tau = 1,dist = "ESN")
# }