G_delta_alpha function

Heavy tail transformation for Lambert W random variables

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

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).

Returns

numeric; same dimension/size as u.