sn (version 0.4-18)

dst: 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, dp = NULL, log = FALSE) 
pst(x, location = 0, scale = 1, shape = 0, df = Inf, dp = NULL, ...)
qst(p, location = 0, scale = 1, shape = 0, df = Inf, tol = 1e-06, dp = NULL, ...)
rst(n = 1, location = 0, scale = 1, shape = 0, df = Inf, dp = NULL)

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, the individual parameters cannot be set.

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.

Details

Typical usages are 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)

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)