View source: R/USER_meanvarFMD.R
meanvarFMD | R Documentation |
It computes the mean vector and variance-covariance matrix for the folded p
-variate Normal, Skew-normal (SN), Extended Skew-normal (ESN) and Student's t-distribution.
meanvarFMD(mu,Sigma,lambda = NULL,tau = NULL,nu = NULL,dist)
mu |
a numeric vector of length p representing the location parameter. |
Sigma |
a numeric positive definite matrix with dimension pxp representing the scale parameter. |
lambda |
a numeric vector of length p representing the skewness parameter for SN and ESN cases. If |
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 |
Normal case by default, i.e., when dist
is not provided. Univariate case is also considered, where Sigma
will be the variance σ^2.
It returns a list with three elements:
mean |
the mean vector of length p |
EYY |
the second moment matrix of dimensions pxp |
varcov |
the variance-covariance matrix of dimensions pxp |
The mean can only be provided when nu
is larger than 2. On the other hand, the varcov matrix can only be provided when nu
is larger than 3.
Degree of freedom must be a positive integer. If nu >= 200
, Normal case is considered."
Christian E. Galarza <cgalarza88@gmail.com> and Victor H. Lachos <hlachos@uconn.edu>
Maintainer: Christian E. Galarza <cgalarza88@gmail.com>
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>.
momentsFMD
, onlymeanTMD
,meanvarTMD
,momentsTMD
, dmvSN
,pmvSN
,rmvSN
, dmvESN
,pmvESN
,rmvESN
, dmvST
,pmvST
,rmvST
, dmvEST
,pmvEST
,rmvEST
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 = meanvarFMD(mu,Sigma,dist="normal") value2 = meanvarFMD(mu,Sigma,nu = 4,dist = "t") value3 = meanvarFMD(mu,Sigma,lambda = c(-2,0,1),dist = "SN") value4 = meanvarFMD(mu,Sigma,lambda = c(-2,0,1),tau = 1,dist = "ESN")
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