MomTrunc (version 4.59)

cdfFMD: Cumulative distribution function for folded multivariate distributions

Description

It computes the cumulative distribution function on x for a folded p-variate Normal, Skew-normal (SN), Extended Skew-normal (ESN) and Student's t-distribution.

Usage

cdfFMD(x,mu,Sigma,lambda = NULL,tau = NULL,dist,nu = NULL)

Arguments

x

vector of length \(p\) where the cdf is evaluated.

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.

dist

represents the folded distribution to be computed. The values are normal, SN , ESN and t for the doubly truncated Normal, Skew-normal, Extended Skew-normal and Student's t-distribution respectively.

nu

It represents the degrees of freedom for the Student's t-distribution.

Value

It returns the distribution value for a single point x.

Details

Normal case by default, i.e., when dist is not provided. Univariate case is also considered, where Sigma will be the variance \(\sigma^2\).

References

Chakraborty, A. K., & Chatterjee, M. (2013). On multivariate folded normal distribution. Sankhya B, 75(1), 1-15.

Kan R. & Robotti C. (2017) On Moments of Folded and Truncated Multivariate Normal Distributions, Journal of Computational and Graphical Statistics, 26:4, 930-934.

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

momentsFMD, meanvarFMD

Examples

# NOT RUN {
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)
cdfFMD(x = c(0.5,0.2,1.0,1.3),mu,Sigma,dist="normal")
cdfFMD(x = c(0.5,0.2,1.0,1.3),mu,Sigma,dist = "t",nu = 4)
cdfFMD(x = c(0.5,0.2,1.0,1.3),mu,Sigma,lambda = c(-2,0,2,1),dist = "SN")
cdfFMD(x = c(0.5,0.2,1.0,1.3),mu,Sigma,lambda = c(-2,0,2,1),tau = 1,dist = "ESN")
# }