R: Input parameters to get a zero mean, unit variance output for...

gamma_01 {LambertW} | R Documentation

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

### Description

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.

### Usage

    gamma_01(gamma, mu.y = 0, sigma.y = 1, distname = "normal")

### Arguments

`gamma` | skewness parameter
`mu.y` | output mean; default: `0`.
`sigma.y` | output standard deviation; default: `1`.
`distname` | string; name of distribution. Currently only supports `"normal"`.

### Value

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.

### Examples

    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)

[Package LambertW version 0.6.7 Index]