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, lower.tail = TRUE, log.p = FALSE)

qskewnorm(p, xi = 0, omega = 1, alpha = 0, lower.tail = TRUE, log.p = FALSE)

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, log.p

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

lower.tail

logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise \(P[X > x]\).

p

vector of probabilities

n

number of random values to return

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. See sn::dsn for more details.

$$f(x;\,\xi,\omega,\alpha) = \frac{2}{\omega}\,\phi\!\left(\frac{x-\xi}{\omega}\right)\Phi\!\left(\alpha\frac{x-\xi}{\omega}\right),$$ where \(\phi\) and \(\Phi\) are the standard normal PDF and CDF.

See also

skewnorm2, skewt, skewt2

Examples

# alpha is skew parameter
x <- rskewnorm(1, alpha = 1)
d <- dskewnorm(x, alpha = 1)
p <- pskewnorm(x, alpha = 1)
q <- qskewnorm(p, alpha = 1)