# sn-st.cumulants: Cumulants of univariate skew-normal and skew-t distributions In sn: The Skew-Normal and Related Distributions Such as the Skew-t

## Description

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

## Usage

 ```1 2``` ``` 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

## References

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

`dsn`, `dsn`
 ```1 2 3 4``` ```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)) ```