param2moment (version 0.1.3)

moment2GH: Solve Tukey \(g\)-&-\(h\) Parameters from Moments

Description

Solve Tukey \(g\)-, \(h\)- and \(g\)-&-\(h\) distribution parameters from mean, standard deviation, skewness and kurtosis.

Usage

moment2GH(mean = 0, sd = 1, skewness, kurtosis)
moment2GH_h_demo(sd = 1, kurtosis)
moment2GH_g_demo(mean = 0, sd = 1, skewness)

Value

Function moment2GH() returns a length-4 numeric

vector

\((A, B, g, h)\).

Function moment2GH_h_demo() returns a length-2 numeric

vector

\((B, h)\).

Function moment2GH_g_demo() returns a length-3 numeric

vector

\((A, B, g)\).

Arguments

mean

numeric scalar, mean \(\mu\), default value 0

sd

numeric scalar, standard deviation \(\sigma\), default value 1

skewness

numeric scalar

kurtosis

numeric scalar

Details

Function moment2GH() solves the location \(A\), scale \(B\), skewness \(g\) and elongation \(h\) parameters of Tukey \(g\)-&-\(h\) distribution, from user-specified mean \(\mu\) (default 0), standard deviation \(\sigma\) (default 1), skewness and kurtosis.

An educational and demonstration function moment2GH_h_demo() solves \((B, h)\) parameters of Tukey \(h\)-distribution, from user-specified \(\sigma\) and kurtosis. This is a non-skewed distribution, thus the location parameter \(A=\mu=0\), and the skewness parameter \(g=0\).

An educational and demonstration function moment2GH_g_demo() solves \((A, B, g)\) parameters of Tukey \(g\)-distribution, from user-specified \(\mu\), \(\sigma\) and skewness. For this distribution, the elongation parameter \(h=0\).

Examples

moment2GH(skewness = .2, kurtosis = .3)

moment2GH_h_demo(kurtosis = .3)

moment2GH_g_demo(skewness = .2)