| gamma_01 {LambertW} | R Documentation |
Computes the input mean μ_x(γ) and standard deviation σ_x(γ) for input X \sim F(x \mid \boldsymbol β) such that the resulting skewed Lambert W x F RV Y with γ has zero-mean and unit-variance. So far works only for Gaussian input and scalar γ.
The function works for any output mean and standard deviation, but μ_y = 0 and σ_y = 1 are set as default as they are the most useful, e.g., to generate a standardized Lambert W white noise sequence.
gamma_01(gamma, mu.y = 0, sigma.y = 1, distname = "normal")
gamma |
skewness parameter |
mu.y |
output mean; default: |
sigma.y |
output standard deviation; default: |
distname |
string; name of distribution. Currently only supports |
A 5-dimensional vector (μ_x(γ), σ_x(γ), γ, 0, 1), where δ = 0 and α = 1 are set for the sake of compatiblity with other functions.
gamma_01(0) # for gamma = 0, input == output, therefore (0,1,0,0,1) # input mean must be slightly negative to get a zero-mean output gamma_01(0.1) # gamma = 0.1 means it is positively skewed gamma_01(1)