sn-st.cumulants {sn}

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.

See Also

dsn, dsn

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))