VGAM (version 1.1-8)

skewnorm: Skew-Normal Distribution

Description

Density and random generation for the univariate skew-normal distribution.

Usage

dskewnorm(x, location = 0, scale = 1, shape = 0, log = FALSE)
rskewnorm(n, location = 0, scale = 1, shape = 0)

Value

dskewnorm gives the density,

rskewnorm generates random deviates.

Arguments

x

vector of quantiles.

n

number of observations. Same as runif.

location

The location parameter \(\xi\). A vector.

scale

The scale parameter \(\omega\). A positive vector.

shape

The shape parameter. It is called \(\alpha\) in skewnormal.

log

Logical. If log=TRUE then the logarithm of the density is returned.

Author

T. W. Yee

Details

See skewnormal, which currently only estimates the shape parameter. More generally here, \(Z = \xi + \omega Y\) where \(Y\) has a standard skew-normal distribution (see skewnormal), \(\xi\) is the location parameter and \(\omega\) is the scale parameter.

References

http://tango.stat.unipd.it/SN.

See Also

skewnormal.

Examples

if (FALSE)  N <- 200  # Grid resolution
shape <- 7; x <- seq(-4, 4, len = N)
plot(x, dskewnorm(x, shape = shape), type = "l", col = "blue", las = 1,
     ylab = "", lty = 1, lwd = 2)
abline(v = 0, h = 0, col = "grey")
lines(x, dnorm(x), col = "orange", lty = 2, lwd = 2)
legend("topleft", leg = c(paste("Blue = dskewnorm(x, ", shape,")", sep = ""),
       "Orange = standard normal density"), lty = 1:2, lwd = 2,
       col = c("blue", "orange"))