sn (version 2.0.0)

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

References

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

See Also

dsn, dsn

Examples

# NOT RUN {
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))
# }