View source: R/USER_momentsTMD.R
momentsTMD | R Documentation |
It computes kappa-th order moments for for some doubly truncated skew-elliptical distributions. It supports the p
-variate Normal, Skew-normal (SN) and Extended Skew-normal (ESN), as well as the Student's-t, Skew-t (ST) and the Extended Skew-t (EST) distribution.
momentsTMD(kappa,lower = rep(-Inf,length(mu)),upper = rep(Inf,length(mu)),mu,Sigma, lambda = NULL,tau = NULL,nu = NULL,dist)
kappa |
moments vector of length p. All its elements must be integers greater or equal to 0. For the Student's-t case, |
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 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 being a positive real number. |
dist |
represents the truncated distribution to be used. The values are |
Univariate case is also considered, where Sigma
will be the variance σ^2.
A data frame containing p+1 columns. The p 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.
If nu >= 300
, 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.
Galarza-Morales, 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>.
Kan, R., & Robotti, C. (2017). On moments of folded and truncated multivariate normal distributions. Journal of Computational and Graphical Statistics, 26(4), 930-934.
onlymeanTMD
,meanvarTMD
,momentsFMD
,meanvarFMD
,dmvSN
,pmvSN
,rmvSN
, dmvESN
,pmvESN
,rmvESN
, dmvST
,pmvST
,rmvST
, dmvEST
,pmvEST
,rmvEST
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 = momentsTMD(c(2,0,1),a,b,mu,Sigma,dist="normal") value2 = momentsTMD(c(2,0,1),a,b,mu,Sigma,dist = "t",nu = 7) value3 = momentsTMD(c(2,0,1),a,b,mu,Sigma,lambda = c(-2,0,1),dist = "SN") value4 = momentsTMD(c(2,0,1),a,b,mu,Sigma,lambda = c(-2,0,1),tau = 1,dist = "ESN") #T cases with kappa scalar (all moments up to 3) value5 = momentsTMD(3,a,b,mu,Sigma,nu = 7,dist = "t") value6 = momentsTMD(3,a,b,mu,Sigma,lambda = c(-2,0,1),nu = 7,dist = "ST") value7 = momentsTMD(3,a,b,mu,Sigma,lambda = c(-2,0,1),tau = 1,nu = 7,dist = "EST")
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