NPflow (version 0.13.5)

mvsnpdf: multivariate Skew-Normal probability density function

Description

multivariate Skew-Normal probability density function

Usage

mvsnpdf(x, xi, sigma, psi, Log = TRUE)

Arguments

x

p x n data matrix with n the number of observations and p the number of dimensions

xi

mean vector or list of mean vectors (either a vector, a matrix or a list)

sigma

variance-covariance matrix or list of variance-covariance matrices (either a matrix or a list)

psi

skew parameter vector or list of skew parameter vectors (either a vector, a matrix or a list)

Log

logical flag for returning the log of the probability density function. Defaults is TRUE.

See Also

mvnpdf, mmvsnpdfC

Examples

mvnpdf(x=matrix(1.96), mean=0, varcovM=diag(1), Log=FALSE)
dnorm(1.96)
mvsnpdf(x=matrix(rep(1.96,1), nrow=1, ncol=1),
      xi=c(0), psi=c(0), sigma=diag(1),
      Log=FALSE
)

mvsnpdf(x=matrix(rep(1.96,2), nrow=2, ncol=1),
      xi=c(0, 0), psi=c(1, 1), sigma=diag(2)
)

N=50000#00
Yn <- rnorm(n=N, mean=0, sd=1)

Z <- rtruncnorm(n=N, a=0, b=Inf, mean=0, sd=1)
eps <- rnorm(n=N, mean=0, sd=1)
psi <- 10
Ysn <- psi*Z + eps

nu <- 1.5
W <- rgamma(n=N, shape=nu/2, rate=nu/2)
Yst=Ysn/sqrt(W)

library(reshape2)
library(ggplot2)
data2plot <- melt(cbind.data.frame(Ysn, Yst))
#pdf(file="ExSNST.pdf", height=5, width=4)
p <- (ggplot(data=data2plot)
     + geom_density(aes(x=value, fill=variable, alpha=variable), col="black")#, lwd=1.1)
     + theme_bw()
     + xlim(-15,100)
     + theme(legend.position="bottom")
     + scale_fill_manual(values=alpha(c("#F8766D", "#00B0F6"),c(0.2,0.45)),
                         name =" ",
                         labels=c("Y~SN(0,1,10)      ", "Y~ST(0,1,10,1.5)")
     )
     + scale_alpha_manual(guide=FALSE, values=c(0.25, 0.45))
     + xlab("Y")
     + ylim(0,0.08)
     + ylab("Density")
     + guides(fill = guide_legend(override.aes = list(colour = NULL)))
     + theme(legend.key = element_rect(colour = "black"))
)
p
#dev.off()