dst {sn} | R Documentation |
Density function, distribution function, quantiles and random number generation for the skew-t (ST) distribution
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)
x |
vector of quantiles. Missing values ( |
p |
vector of probabililities. |
xi |
vector of location parameters. |
omega |
vector of scale parameters; must be positive. |
alpha |
vector of slant parameters. With |
nu |
degrees of freedom (scalar); default is |
dp |
a vector of length 4, whose elements represent location, scale
(positive), slant and degrees of freedom, respectively. If |
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
|
... |
additional parameters passed to |
Density (dst
), probability (pst
), quantiles (qst
)
and random sample (rst
) from the skew-t distribution with given
xi
, omega
, alpha
and nu
parameters.
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)
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.
Azzalini, A. and Capitanio, A. (2014). The Skew-normal and Related Families. Cambridge University Press, IMS Monographs series.
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)