W_delta {LambertW} | R Documentation |
Inverse transformation for Lambert W RVs. Principal and non-principal branch.
W_delta(z, delta = 0) W_delta_1(z, delta = 0)
z |
a numeric vector of real values. |
delta |
skewness parameter; by default delta = 0 , which implies W_delta(z) = W_delta_1(z) = z . |
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)
.
Computes frac{1}{delta} W(delta z). If z is a vector, so is the output.
Georg M. Goerg
Goerg, G.M. (2009). “Lambert W Random Variables - A new class of skewed distribution functions”. Unpublished