dst {sn}R Documentation

Skew-t Distribution

Description

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

Usage

dst(x, xi=0, omega=1, alpha=0, nu=Inf, dp=NULL, log=FALSE) 
pst(x, xi=0, omega=1, alpha=0, nu=Inf, dp=NULL, ...)
qst(p, xi=0, omega=1, alpha=0, nu=Inf, tol=1e-08, dp=NULL, ...)
rst(n=1, xi=0, omega=1, alpha=0, nu=Inf, dp=NULL)

Arguments

x

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

p

vector of probabililities.

xi

vector of location parameters.

omega

vector of scale parameters; must be positive.

alpha

vector of slant parameters. With pst and qst, it must be of length 1.

nu

degrees of freedom (scalar); default is nu=Inf which corresponds to the skew-normal distribution.

dp

a vector of length 4, whose elements represent location, scale (positive), slant and degrees of freedom, 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 xi, omega, alpha and nu parameters.

Details

Typical usages are

dst(x, xi=0, omega=1, alpha=0, nu=Inf, log=FALSE)
dst(x, dp=, log=FALSE)
pst(x, xi=0, omega=1, alpha=0, nu=Inf, ...)
pst(x, dp=, log=FALSE)
qst(p, xi=0, omega=1, alpha=0, nu=Inf, tol=1e-8, ...)
qst(x, dp=, log=FALSE)
rst(n=1, xi=0, omega=1, alpha=0, nu=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 alpha parameter which regulates skewness; when alpha=0, the skew-t distribution reduces to the usual Student's t distribution. When nu=Inf, it reduces to the skew-normal distribution. A multivariate version of the distribution exists. See Chapter 4 of the reference below for additional information.

References

Azzalini, A. and Capitanio, A. (2014). The Skew-normal and Related Families. Cambridge University Press, IMS Monographs series.

See Also

dmst, dsn

Examples

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


[Package sn version 1.0-0 Index]