sn: sn-st.cumulants – R documentation

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sn-st.cumulants

Cumulants of univariate skew-normal and skew-t distributions

Description

Compute cumulants of univariate (extended) skew-normal and skew-t distributions up to a given order.

Usage

sn.cumulants(xi=0, omega=1, alpha=0, tau=0, dp=NULL, n=4)
  st.cumulants(xi=0, omega=1, alpha=0, nu=Inf, dp=NULL, n=4)

Arguments

`xi`	location parameters (numeric vector).
`omega`	scale parameters (numeric vector, positive).
`alpha`	slant parameters (numeric vector).
`tau`	hidden mean parameter (numeric scalar).
`nu`	degrees of freedom (numeric scalar, positive); the default value is `nu=Inf` which corresponds to the skew-normal distribution.
`dp`	a vector containing the appropriate set of parameters. If `dp` is not `NULL`, the individual parameters must not be supplied.
`n`	maximal order of the cumulants. For `st.cumulants` and for `sn.cumulants` with `tau!=0` (ESN distribution), it cannot exceed 4.

Value

A vector of length n or a matrix with n columns, in case the input values are vectors.

Background

See Sections 2.1.4, 2.2.3 and 4.3.1 of the reference below

Author(s)

Adelchi Azzalini

References

Azzalini, A. with the collaboration of Capitanio, A. (2014). The Skew-Normal and Related Families. Cambridge University Press, IMS Monographs series.

Examples

sn.cumulants(omega=2, alpha=c(0, 3, 5, 10), n=5)
sn.cumulants(dp=c(0, 3, -8), n=6)
st.cumulants(dp=c(0, 3, -8, 5), n=6) # only four of them are computed
st.cumulants(dp=c(0, 3, -8, 3))

sn

The Skew-Normal and Related Distributions Such as the Skew-t and the SUN

v2.0.0

GPL-2 | GPL-3

Authors

Adelchi Azzalini [aut, cre] (<https://orcid.org/0000-0002-7583-1269>)

Initial release

2021-03-28