dst {sn}R Documentation

Skew-t Distribution

Description

Density function, distribution function and random number generation for the skew-t (ST) distribution.

Usage

dst(x, location=0, scale=1, shape=0, df=Inf, log=FALSE)
dst(x, dp=, log=FALSE)
pst(x, location=0, scale=1, shape=0, df=Inf, ...)
pst(x, dp=, log=FALSE)
qst(p, location=0, scale=1, shape=0, df=Inf, tol=1e-8, ...)
qst(x, dp=, log=FALSE)
rst(n=1, location=0, scale=1, shape=0, df=Inf)
rst(x, dp=, log=FALSE)

Arguments

x vector of quantiles. Missing values (NAs) are allowed.
p vector of probabililities
location vector of location parameters.
scale vector of (positive) scale parameters.
shape vector of shape parameters. With pst and qst, it must be of length 1.
df degrees of freedom (scalar); default is df=Inf which corresponds to the skew-normal distribution.
dp a vector of length 4, whose elements represent location, scale (positive), shape and df, respectively. If dp is specified, this overrides the specification of the other parameters.
n sample size.
log logical; if TRUE, densities are given as log-densities.
tol a scalar value which regulates the accuracy of the result of qsn.
... additional parameters passed to integrate.

Value

Density (dst), probability (pst), quantiles (qst) and random sample (rst) from the skew-t distribution with given location, scale, shape and df parameters.

Background

The family of skew-t distributions is an extension of the Student's t family, via the introduction of a shape parameter which regulates skewness; when shape=0, the skew-t distribution reduces to the usual Student's t distribution. When df=Inf, it reduces to the skew-normal distribution. A multivariate version of the distribution exists. See the reference below for additional information.

References

Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew-t distribution. J.Roy. Statist. Soc. B 65, 367–389.

See Also

dmst, dsn, psn

Examples

pdf <- dst(seq(-4,4,by=0.1), shape=3, df=5)
rnd <- rst(100, 5, 2, -5, 8)
q <- qst(c(0.25,0.5,0.75), shape=3, df=5)
pst(q, shape=3, df=5)  # must give back c(0.25,0.5,0.75)


[Package sn version 0.4-4 Index]