Skew-t Distribution

Density function, distribution function and random number generation for the skew-\(t\) (ST) distribution. Functions copied from sn CRAN library v0.4.18 for argument name compatibility with st.mle function from the same version.

Usage

dst(x, location = 0, scale = 1, shape = 0, df = Inf, dp = NULL, log = FALSE)

rst(n = 1, location = 0, scale = 1, shape = 0, df = Inf, dp = NULL)

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,
  ...
)

Arguments

x: vector of quantiles. Missing values (NAs) are allowed.
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.
log: logical; if TRUE, densities are given as log-densities.
n: sample size.
...: additional parameters passed to integrate.
p: vector of probabililities
tol: a scalar value which regulates the accuracy of the result of qsn.

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


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)

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.

Examples