sn (version 1.0-0)

dsn: Skew-Normal Distribution

Description

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

Usage

dsn(x, xi=0, omega=1, alpha=0, tau=0, dp=NULL, log=FALSE)
psn(x, xi=0, omega=1, alpha=0, tau=0, dp=NULL, engine, ...)
qsn(p, xi=0, omega=1, alpha=0, tau=0, dp=NULL, tol=1e-8,  ...) 
rsn(n=1, xi=0, omega=1, alpha=0, tau=0,  dp=NULL)

Arguments

x

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

p

vector of probabilities. Missing values (NAs) are allowed

xi

vector of location parameters.

omega

vector of scale parameters; must be positive.

alpha

vector of slant parameters; +/- Inf is allowed. With psn and qsn, it must be of length 1 if engine="T.Owen".

tau

a single value representing the `hidden mean' parameter of the ESN distribution; tau=0 (default) corresponds to a SN distribution.

dp

a vector of length 3 (in the SN case) or 4 (in the ESN case), whose components represent the individual parameters described above. If dp is specified, the individual parameters cannot be set.

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.

engine

a character string which selects the computing engine; this is either "T.Owen" or "biv.nt.prob", the latter from package mnormt. If tau != 0 or length(alpha)>1, "biv.nt.pro

...

additional parameters passed to T.Owen

Value

• density (dsn), probability (psn), quantile (qsn) or random sample (rsn) from the skew-normal distribution with given xi, omega and alpha parameters or from the extended skew-normal if tau!=0

Details

Typical usages are dsn(x, xi=0, omega=1, alpha=0, log=FALSE) dsn(x, dp=, log=FALSE) psn(x, xi=0, omega=1, alpha=0, ...) psn(x, dp=, ...) qsn(p, xi=0, omega=1, alpha=0, tol=1e-8, ...) qsn(x, dp=, ...) rsn(n=1, xi=0, omega=1, alpha=0) rsn(x, dp=) psn and qsn make use of function T.Owen or biv.nt.prob

Background

The family of skew-normal distributions is an extension of the normal family, via the introdution of a alpha parameter which regulates asymmetry; when alpha=0, the skew-normal distribution reduces to the normal one. The density function of the SN distribution in the normalized case having xi=0 and omega=1 is 2*dnorm(x)*pnorm(alpha*x). An early discussion of the skew-normal distribution is given by Azzalini (1985); see Section 3.3 for the ESN variant, up to a slight difference in the parameterization. An updated extensive account is provided by Chapter 2 of Azzalini and Capitanio (2014); the ESN variant is presented Section 2.2. A multivariate version of the distribution is examined in Chapter 5.

References

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

Azzalini, A. with the collaboration of Capitanio, A. (2014). The Skew-Normal and Related Families. Cambridge University Press, IMS Monographs series.

See Also

Functions used by psn: T.Owen, biv.nt.prob Related distributions: dmsn, dst, dmst

Examples

pdf <- dsn(seq(-3, 3, by=0.1), alpha=3)
cdf <- psn(seq(-3, 3, by=0.1), alpha=3)
q <- qsn(seq(0.1, 0.9, by=0.1), alpha=-2)
r <- rsn(100, 5, 2, 5)