dprmvST {MomTrunc} | R Documentation |
Multivariate Skew t Density, Probablilities and Random Deviates Generator
Description
These functions provide the density function, probabilities and a random number
generator for the multivariate skew t (EST) distribution with mean vector mu
, scale matrix Sigma
, skewness parameter lambda
and degrees of freedom nu
.
Usage
dmvST(x,mu=rep(0,length(lambda)),Sigma=diag(length(lambda)),lambda,nu)
pmvST(lower = rep(-Inf,length(lambda)),upper=rep(Inf,length(lambda)),
mu = rep(0,length(lambda)),Sigma,lambda,nu,log2 = FALSE)
rmvST(n,mu=rep(0,length(lambda)),Sigma=diag(length(lambda)),lambda,nu)
Arguments
x |
vector or matrix of quantiles. If |
n |
number of observations. |
lower |
the vector of lower limits of length |
upper |
the vector of upper limits of length |
mu |
a numeric vector of length |
Sigma |
a numeric positive definite matrix with dimension |
lambda |
a numeric vector of length |
nu |
It represents the degrees of freedom of the Student's t-distribution. |
log2 |
a boolean variable, indicating if the log2 result should be returned. This is useful when the true probability is too small for the machine precision. |
Value
dmvST
gives the density, pmvST
gives the distribution function, and rmvST
generates random deviates for the Multivariate Skew-t
Distribution.
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>.
Genz, A., (1992) "Numerical computation of multivariate normal probabilities," Journal of Computational and Graphical Statistics, 1, 141-149 <doi:10.1080/10618600.1992.10477010>.
See Also
dmvST
, pmvST
, rmvST
, meanvarFMD
,meanvarTMD
,momentsTMD
Examples
#Univariate case
dmvST(x = -1,mu = 2,Sigma = 5,lambda = -2,nu=4)
rmvST(n = 100,mu = 2,Sigma = 5,lambda = -2,nu=4)
#Multivariate case
mu = c(0.1,0.2,0.3,0.4)
Sigma = matrix(data = c(1,0.2,0.3,0.1,0.2,1,0.4,-0.1,0.3,0.4,1,0.2,0.1,-0.1,0.2,1),
nrow = length(mu),ncol = length(mu),byrow = TRUE)
lambda = c(-2,0,1,2)
#One observation
dmvST(x = c(-2,-1,0,1),mu,Sigma,lambda,nu=4)
rmvST(n = 100,mu,Sigma,lambda,nu=4)
#Many observations as matrix
x = matrix(rnorm(4*10),ncol = 4,byrow = TRUE)
dmvST(x = x,mu,Sigma,lambda,nu=4)
lower = rep(-Inf,4)
upper = c(-1,0,2,5)
pmvST(lower,upper,mu,Sigma,lambda,nu=4)