delta.01 {LambertW}R Documentation

Input parameters to get a zero mean, unit variance output for a given delta

Description

This function computes the input mean μ_x(delta) and standard deviation σ_x(delta) such that the resulting Lambert W Gaussian RV Y has zero mean, and unit variance for any given delta. Although, in principle, the function allows any output mean and variance, the default values μ_y = 0 and σ_y = 1 are the most useful, e.g. to generate a standardized LambertW white noise sequence.

So far only for Gaussian input.

Usage

delta.01(delta, mu_y=0, sigma_y=1)

Arguments

delta skewness parameter
mu_y output mean; default: 0
sigma_y output standard deviation; default: 1

Value

The 3-dimensional vector (delta, μ_x(delta), σ_x(delta)).

Author(s)

Georg M. Goerg

References

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 Unpublished

Examples

delta.01(0)     # for delta = 0, input == output, therefore (0,0,1)
delta.01(0.1)   # delta>0 (positively skewed): input mean must be 
                # slightly negative to get a zero-mean output
delta.01(1)

[Package LambertW version 0.1.9 Index]