MomTrunc (version 4.59)

pmvESN: Multivariate Extended-Skew Normal Probabilities

Description

Computes the distribution function of the multivariate extended-skew normal (ESN) and skew-normal (SN, as particular case) distribution for arbitrary limits, mean vector \(mu\), scale matrix \(sigma\), skewness parameter \(lambda\) and extension parameter \(tau\).

Usage

pmvESN(lower = rep(-Inf,length(lambda)),upper=rep(Inf,length(lambda)),
        mu = rep(0,length(lambda)),Sigma,lambda,tau, ...)

Arguments

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 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.

...

Arguments passed to the pmvnorm fucntion from the mvtnorm, for instance, algorithm.

Value

The evaluated distribution function is returned.

Details

This code uses the pmvnorm function from mvtnorm package. For the normal case (all lambda and tau equal to zero), it is better to use pmvnorm directly.

References

Genz, A. and Bretz, F. (2009), Computation of Multivariate Normal and t Probabilities. Lecture Notes in Statistics, Vol. 195. Springer-Verlag, Heidelberg.

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

dmvESN,rmvESN, meanvarFMD,meanvarTMD,momentsTMD

Examples

# NOT RUN {
lower = rep(-Inf,4)
upper = c(-1,0,2,5)
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
pmvESN(lower,upper,mu,Sigma,lambda,tau)
# }