W_delta {LambertW}R Documentation

Inverse transformation for Lambert W random variables

Description

Inverse transformation for Lambert W RVs. Principal and non-principal branch.

Usage

W_delta(z, delta = 0)
W_delta_1(z, delta = 0)

Arguments

z a numeric vector of real values.
delta skewness parameter; by default delta = 0, which implies W_delta(z) = W_delta_1(z) = z.

Details

A Lambert W RV is defined using the transformation

z = u exp(delta u)=:H_{delta}(u), quad delta in R.

The function W_delta(z) (and W_delta_1(z)) are the inverse functions of this transformation. If delta = 0, then z = u and the inverse transformation also equals the identity.

If delta neq 0, the inverse transformation can be computed by

W_{delta}(z) = frac{1}{delta} W(delta z).

Same holds for W_delta_1(z).

Value

Computes frac{1}{delta} W(delta z). If z is a vector, so is the output.

Author(s)

Georg M. Goerg

References

Goerg, G.M. (2009). “Lambert W Random Variables - A new class of skewed distribution functions”. Unpublished


[Package LambertW version 0.1.9 Index]