sn: galton_moors2alpha_nu – R documentation

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galton_moors2alpha_nu

Mapping of the (Galton-Bowley, Moors) measures to the (alpha, nu) parameters of a ST distribution

Description

Given a pair of (Galton-Bowley, Moors) measures of skewness and kurtosis for a given sample, a pair of values (alpha, nu) are found such that a skew-t (ST) distribution with these slant and tail-weight parameter has its (Galton-Bowley, Moors) measures equal to the input values. This function is mainly intended for internal package usage.

Usage

galton_moors2alpha_nu(galton, moors, quick = TRUE, move.in = TRUE, verbose = 0, 
  abstol = 1e-04)

Arguments

`galton`	a numeric value, representing a Galton-Bowley measure
`moors`	a numeric value, representing a Moors measure
`quick`	a logical value; if `TRUE`, a quick mapping is performed
`move.in`	if the input values `(galton, moors)` are outside the feasible ST region, a suitable point within the feasible area is returned
`verbose`	a numeric value which regulates the amount of printed detail
`abstol`	the tolerance value of the mapping, only relevant is `quick=FALSE`

Details

For background information about the Galton-Bowley's and the Moors measures, see the documentation of fournum. The working of the mapping by described in Azzalini and Salehi (2020).

Value

a named vector of length two, with one or more descriptive attributes

Note

This function is mainly intended for internal package usage. Specifically it is used by st.prelimFit.

Author(s)

Adelchi Azzalini

References

Azzalini, A. and Salehi, M. (2020). Some computational aspects of maximum likelihood estimation of the skew-t distribution. In: Computational and Methodological Statistics and Biostatistics, edited by Andriëtte Bekker, Ding-Geng Chen and Johannes T. Ferreira. Springer. DOI: 10.1007/978-3-030-42196-0

Examples

galton_moors2alpha_nu(0.5, 3, quick=FALSE)  # input in the feasible area
galton_moors2alpha_nu(0.5, 3)    # very similar output, much more quickly
galton_moors2alpha_nu(0.5, 0.5)  # input outside the feasible area

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