momentsFMD {MomTrunc} | R Documentation |
Moments for folded multivariate distributions
Description
It computes the kappa-th order moments for the folded p
-variate Normal, Skew-normal (SN), Extended Skew-normal (ESN) and Student's t-distribution. It also output other lower moments involved in the recurrence approach.
Usage
momentsFMD(kappa,mu,Sigma,lambda = NULL,tau = NULL,nu = NULL,dist)
Arguments
kappa |
moments vector of length |
mu |
a numeric vector of length |
Sigma |
a numeric positive definite matrix with dimension |
lambda |
a numeric vector of length |
tau |
It represents the extension parameter for the ESN distribution. If |
nu |
It represents the degrees of freedom for the Student's t-distribution. Must be an integer greater than 1. |
dist |
represents the folded distribution to be computed. The values are |
Details
Univariate case is also considered, where Sigma
will be the variance .
Value
A data frame containing columns. The
first containing the set of combinations of exponents summing up to
kappa
and the last column containing the the expected value. Normal cases (ESN, SN and normal) return prod(kappa)+1
moments while the Student's t-distribution case returns all moments of order up to kappa
. See example section.
Warning
For the Student-t cases, including ST and EST, kappa
- order moments exist only for
kappa < nu
.
Note
Degrees of freedom must be a positive integer. If nu >= 300
, Normal case is considered."
Author(s)
Christian E. Galarza <cgalarza88@gmail.com> and Victor H. Lachos <hlachos@uconn.edu>
Maintainer: Christian E. Galarza <cgalarza88@gmail.com>
References
Galarza, C. E., Lin, T. I., Wang, W. L., & Lachos, V. H. (2021). On moments of folded and truncated multivariate Student-t distributions based on recurrence relations. Metrika, 84(6), 825-850 <doi:10.1007/s00184-020-00802-1>.
Galarza, C. E., Matos, L. A., Dey, D. K., & Lachos, V. H. (2022a). "On moments of folded and doubly truncated multivariate extended skew-normal distributions." Journal of Computational and Graphical Statistics, 1-11 <doi:10.1080/10618600.2021.2000869>.
Galarza, C. E., Matos, L. A., Castro, L. M., & Lachos, V. H. (2022b). Moments of the doubly truncated selection elliptical distributions with emphasis on the unified multivariate skew-t distribution. Journal of Multivariate Analysis, 189, 104944 <doi:10.1016/j.jmva.2021.104944>.
See Also
meanvarFMD
, onlymeanTMD
,meanvarTMD
,momentsTMD
, dmvSN
,pmvSN
,rmvSN
, dmvESN
,pmvESN
,rmvESN
, dmvST
,pmvST
,rmvST
, dmvEST
,pmvEST
,rmvEST
Examples
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(3,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")
#T case with kappa vector input
value5 = momentsFMD(c(2,0,1),mu,Sigma,dist = "t",nu = 7)