G_delta_alpha {LambertW}

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.