MomTrunc (version 4.59)

drmvESN: Multivariate Extended-Skew Normal Density and Random Deviates

Description

These functions provide the density function and a random number generator for the multivariate extended-skew normal (ESN) and skew-normal (SN, as particular case) distribution with mean vector \(mu\), scale matrix \(sigma\), skewness parameter \(lambda\) and extension parameter \(tau\).

Usage

dmvESN(x,mu=rep(0,length(lambda)),Sigma=diag(length(lambda)),lambda,tau=0)
rmvESN(n,mu=rep(0,length(lambda)),Sigma=diag(length(lambda)),lambda,tau=0)

Arguments

x

vector or matrix of quantiles. If x is a matrix, each row is taken to be a quantile.

n

number of observations.

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 SN and ESN cases. If lambda == 0, the ESN/SN reduces to a normal (symmetric) distribution.

tau

It represents the extension parameter for the ESN distribution. If tau == 0, the ESN reduces to a SN distribution.

Details

The rmvESN function is based on a rejection algorithm, so for small values of tau, that is, when \(\tau \le -2\sqrt{1+\sum{\lambda_i^2}}\), it is possible that the algorithm return less than the n observations and also take more time than usual, due to the high rejection rate.

References

C.E. Galarza, L.A. Matos, D.K. Dey & V.H. Lachos. (2019) On Moments of Folded and Truncated Multivariate Extended Skew-Normal Distributions. Technical report. ID 19-14. University of Connecticut.

See Also

pmvESN, meanvarFMD,meanvarTMD,momentsTMD

Examples

# NOT RUN {
#Univariate case
dmvESN(x = -1,mu = 2,Sigma = 5,lambda = -2,tau = 0.5)
rmvESN(n = 100,mu = 2,Sigma = 5,lambda = -2,tau = 0.5)
#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
dmvESN(x = c(-2,-1,0,1),mu,Sigma,lambda,tau)
rmvESN(n = 100,mu,Sigma,lambda,tau)
#Many observations as matrix
x = matrix(rnorm(4*10),ncol = 4,byrow = TRUE)
dmvESN(x = x,mu,Sigma,lambda,tau)
# }