| delta_01 {LambertW} | R Documentation |
Computes the input mean μ_x(δ) and standard deviation σ_x(δ) for input X \sim F(x \mid \boldsymbol β) such that the resulting heavy-tail Lambert W x F RV Y with δ has zero-mean and unit-variance. So far works only for Gaussian input and scalar δ.
The function works for any output mean and standard deviation, but default values are μ_y = 0 and σ_y = 1 since they are the most useful, e.g., to generate a standardized Lambert W white noise sequence.
delta_01(delta, mu.y = 0, sigma.y = 1, distname = "normal")
delta |
scalar; heavy-tail parameter. |
mu.y |
output mean; default: |
sigma.y |
output standard deviation; default: |
distname |
string; distribution name. Currently this function only supports
|
5-dimensional vector (μ_x(δ), σ_x(δ), 0, δ, 1), where γ = 0 and α = 1 are set for the sake of compatiblity with other functions.
delta_01(0) # for delta = 0, input == output, therefore (0,1,0,0,1) # delta > 0 (heavy-tails): # Y is symmetric for all delta: # mean = 0; however, sd must be smaller delta_01(0.1) delta_01(1/3) # only moments up to order 2 exist delta_01(1) # neither mean nor variance exist, thus NA