dprmvEST function

Multivariate Extended-Skew t Density, Probablilities and Random Deviates Generator

These functions provide the density function, probabilities and a random number generator for the multivariate extended-skew t (EST) distribution with mean vector mu, scale matrix Sigma, skewness parameter lambda, extension parameter tau and degrees of freedom nu.

dmvEST(x,mu=rep(0,length(lambda)),Sigma=diag(length(lambda)),lambda,tau=0,nu)
pmvEST(lower = rep(-Inf,length(lambda)),upper=rep(Inf,length(lambda)),
        mu = rep(0,length(lambda)),Sigma,lambda,tau,nu,log2 = FALSE)
rmvEST(n,mu=rep(0,length(lambda)),Sigma=diag(length(lambda)),lambda,tau,nu)

Arguments

• x: vector or matrix of quantiles. If x is a matrix, each row is taken to be a quantile.
• n: number of observations.
• 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 $p$x$p$ representing the scale parameter.
• lambda: a numeric vector of length $p$ representing the skewness parameter for ST and EST cases. If lambda == 0, the EST/ST reduces to a t (symmetric) distribution.
• tau: It represents the extension parameter for the EST distribution. If tau == 0, the EST reduces to a ST distribution.
• 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.

Returns

dmvEST gives the density, pmvEST gives the distribution function, and rmvEST generates random deviates for the Multivariate Extended-Skew-$t$ Distribution.

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., 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.

Author(s)

Christian E. Galarza <cgalarza88@gmail.com > and Victor H. Lachos <hlachos@uconn.edu >

Maintainer: Christian E. Galarza <cgalarza88@gmail.com >

See Also

dmvST, pmvST, rmvST, meanvarFMD,meanvarTMD,momentsTMD

Examples

#Univariate case
dmvEST(x = -1,mu = 2,Sigma = 5,lambda = -2,tau = 0.5,nu=4)
rmvEST(n = 100,mu = 2,Sigma = 5,lambda = -2,tau = 0.5,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)
tau = 2
#One observation
dmvEST(x = c(-2,-1,0,1),mu,Sigma,lambda,tau,nu=4)
rmvEST(n = 100,mu,Sigma,lambda,tau,nu=4)
#Many observations as matrix
x = matrix(rnorm(4*10),ncol = 4,byrow = TRUE)
dmvEST(x = x,mu,Sigma,lambda,tau,nu=4)

lower = rep(-Inf,4)
upper = c(-1,0,2,5)
pmvEST(lower,upper,mu,Sigma,lambda,tau,nu=4)