R: Heavy tail transformation for Lambert W random variables

G_delta_alpha {LambertW} | R Documentation

## Heavy tail transformation for Lambert W random variables

### Description

Heavy-tail Lambert W RV transformation: G_{δ, α}(u) = u \exp(\frac{δ}{2} (u^2)^{α}). Reduces to Tukey's h distribution for α = 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)^{α}; default `alpha = 1` (Tukey's h).

### Value

numeric; same dimension/size as `u`.

[Package LambertW version 0.6.7 Index]