Skew normal distribution

Density, distribution function, quantile function and random generation for the skew normal distribution.

Usage

dskewnorm(x, xi = 0, omega = 1, alpha = 0, log = FALSE)

pskewnorm(q, xi = 0, omega = 1, alpha = 0, ...)

qskewnorm(p, xi = 0, omega = 1, alpha = 0, ...)

rskewnorm(n, xi = 0, omega = 1, alpha = 0)

Arguments

x, q

vector of quantiles

xi

location parameter

omega

scale parameter, must be positive.

alpha

skewness parameter, +/- Inf is allowed.

log

logical; if TRUE, probabilities/ densities \(p\) are returned as \(\log(p)\).

...

additional parameters to be passed to the sn package functions for pskewnorm and qskewnorm.

p

vector of probabilities

n

number of observations. If length(n) > 1, the length is taken to be the number required.

Value

dskewnorm gives the density, pskewnorm gives the distribution function, qskewnorm gives the quantile function, and rskewnorm generates random deviates.

Details

This implementation of dskewnorm allows for automatic differentiation with RTMB while the other functions are imported from the sn package.

Examples

x = rskewnorm(1)
d = dskewnorm(x)
p = pskewnorm(x)
q = qskewnorm(p)