sn (version 0.33)

dsn: Skew-Normal Distribution

Description

Density function, distribution function, quantiles and random number generation for the skew-normal (SN) distribution.

Usage

dsn(x, location=0, scale=1, shape=0, log=FALSE)
psn(x, location=0, scale=1, shape=0, ...)
qsn(p, location=0, scale=1, shape=0, tol=1e-8, ...)
rsn(n=1, location=0, scale=1, shape=0)

Arguments

x

vector of quantiles. Missing values (NAs) and Inf's are allowed.

p

vector of probabilities. Missing values (NAs) are allowed.

location

vector of location parameters.

scale

vector of (positive) scale parameters.

shape

vector of shape parameters. With psn and qsn, it must be of length 1.

n

sample size.

tol

a scalar value which regulates the accuracy of the result of qsn.

log

logical flag used in dsn (default FALSE). When TRUE, the logarithm of the density values is returned.

...

additional parameters passed to T.Owen

Value

• density (dsn), probability (psn), quantile (qsn) or random sample (rsn) from the skew-normal distribution with given location, scale and shape parameters.

Background

The family of skew-normal distributions is an extension of the normal family, via the introdution of a shape parameter which regulates skewness; when shape=0, the skew-normal distribution reduces to the normal one. The density of the SN distribution in the "standard" case having location=0 and scale=1 is 2*dnorm(x)*pnorm(shape*x). A multivariate version of the distribution exists. See the references below for additional information.

Details

psn and qsn make use of function T.Owen

References

Azzalini, A. (1985). A class of distributions which includes the normal ones. Scand. J. Statist. 12, 171-178.

Azzalini, A. and Dalla Valle, A. (1996). The multivariate skew-normal distribution. Biometrika 83, 715--726.

See Also

T.Owen, dmsn, dst

Examples

pdf <- dsn(seq(-3,3,by=0.1), shape=3)
cdf <- psn(seq(-3,3,by=0.1), shape=3)
qu <- qsn(seq(0.1,0.9,by=0.1), shape=-2)
rn <- rsn(100, 5, 2, 5)