MomTrunc (version 4.59)

momentsFMD: Moments for folded multivariate distributions

Description

It computes the kappa-th raw moment for the folded p-variate Normal, Skew-normal (SN), Extended Skew-normal (ESN) and Student's t-distribution. It also output some other lower moments (than kappa) involved in the recurrence approach.

Usage

momentsFMD(kappa,mu,Sigma,lambda = NULL,tau = NULL,dist,nu = NULL)

Arguments

kappa

moments vector of length \(p\). All its elements must be integers greater or equal to \(0\).

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

A data frame containing \(p+1\) columns. The \(p\) first containing the set of moments involved in the recursive approach and the last column containing the expected value.

Normal cases (ESN, SN and normal) return prod(kappa)+1 moments while the Student's t-distribution case returns sum(kappa)+1. See example section.

Warning

For the Student-t case, the kappa-\(th\) moment can only be computed when sum(kappa) \(\le\) nu-2.

Details

Normal case by default, i.e., when dist is not provided. Univariate case is also considered, where Sigma will be the variance \(\sigma^2\).

References

Kan, R., & Robotti, C. (2017). On Moments of Folded and Truncated Multivariate Normal Distributions. Journal of Computational and Graphical Statistics, (just-accepted).

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.

See Also

meanvarFMD, meanvarFMD,momentsTMD,meanvarTMD,cdfFMD,dmvESN,rmvESN

Examples

# NOT RUN {
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 = momentsFMD(c(2,0,1),mu,Sigma,dist="normal")
value2 = momentsFMD(c(0,2,0),mu,Sigma,dist = "t",nu = 7)
value3 = momentsFMD(c(2,0,1),mu,Sigma,lambda = c(-2,0,1),dist = "SN")
value4 = momentsFMD(c(2,0,1),mu,Sigma,lambda = c(-2,0,1),tau = 1,dist = "ESN")
# }