LambertW (version 0.6.4)

G_delta_alpha: Heavy tail transformation for Lambert W random variables

Description

Heavy-tail Lambert W RV transformation: $G_{\delta ,\alpha }(u)=u\exp (\frac{\delta }{2}(u^2{)}^{\alpha })$. Reduces to Tukey's h distribution for $\alpha =1$ (G_delta) and Gaussian input.

Usage

G_delta_alpha(u, delta = 0, alpha = 1)
G_delta(u, delta = 0)
G_2delta_2alpha(u, delta = c(0, 0), alpha = c(1, 1))

Arguments

u

a numeric vector of real values.

delta

heavy tail parameter; default delta = 0, which implies G_delta_alpha(u) = u.

alpha

exponent in $(u^2{)}^{\alpha }$; default alpha = 1 (Tukey's h).

Value

numeric; same dimension/size as u.