Skewt Distribution
Description
Density function, distribution function and random number generation
for the skewt (ST) distribution. Functions copied from sn
CRAN library v0.4.18 for argument name compatibility with st.mle
function from the same version.
Usage
1 2 3 4 
Arguments
x 
vector of quantiles. Missing values ( 
p 
vector of probabililities 
location 
vector of location parameters. 
scale 
vector of (positive) scale parameters. 
shape 
vector of shape parameters. With 
df 
degrees of freedom (scalar); default is 
dp 
a vector of length 4, whose elements represent location, scale (positive),
shape and df, respectively. If 
n 
sample size. 
log 
logical; if TRUE, densities are given as logdensities. 
tol 
a scalar value which regulates the accuracy of the result of

... 
additional parameters passed to 
Value
Density (dst
), probability (pst
), quantiles (qst
)
and random sample (rst
) from the skewt distribution with given
location
, scale
, shape
and df
parameters.
Details
Typical usages are
1 2 3 4 5 6 7 8  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=1e8, ...)
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 skewt distributions is an extension of the Student's t
family, via the introduction of a shape
parameter which regulates
skewness; when shape=0
, the skewt distribution reduces to the
usual Student's t distribution. When df=Inf
, it reduces to the
skewnormal 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 skewt distribution. J.Roy. Statist. Soc. B 65, 367–389.
See Also
st.mle
Examples
1 2 3 4 