R: Cumulants of univariate skew-normal and skew-t distributions

sn-st.cumulants {sn} | R Documentation

## 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 0 `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))

[Package sn version 1.5-0 Index]