sn (version 2.1.1)

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, galton_moors2alpha_nu delivers values (\(alpha\), \(nu\)) 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. Its simplified version galton2alpha uses only a Galton-Bowley measure to deliver a \(alpha\) value, assuming a SN distribution. These functions are mainly intended for internal package usage.

Usage

galton_moors2alpha_nu(galton, moors, quick = TRUE, move.in = TRUE, verbose = 0, 
  abstol = 1e-04)
galton2alpha(galton, move.in = TRUE)

Value

for galton_moors2alpha_nu, named vector of length two, with one or more descriptive attributes; for galton2alpha, a single alpha value.

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

Author

Adelchi Azzalini

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).

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

See Also

fournum, st.prelimFit

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