R: Get bounds for gamma

get_gamma_bounds {LambertW} | R Documentation

## Get bounds for gamma

### Description

`get_gamma_bounds` returns lower and upper bounds for γ, so that the observed data range falls within the theoretical bounds of the support of the distribution. This is only important for location family input.

### Usage

    get_gamma_bounds(y, tau)

### Arguments

`y` | a numeric vector of real values (the observed data).
`tau` | named vector τ which defines the variable transformation. Must have at least `'mu_x'` and `'sigma_x'` element; see `complete_tau` for details.

### Details

Skewed Lambert W\times F distributions have parameter-dependent support for location family input. Thus the parameter γ must be bounded such that the observed data is within the theoretical support of the distribution. This theoretical bounds are determined by the Lambert W function (`W`), which has only real-valued solutions for z ≥q -1 / \exp(1). Thus, `W_gamma` has real-valued solutions only for z ≥q -1 / \exp(1) γ These lower and upper bounds are determined by minimum and maxiumum of the normalized data \mathbf{z} = (\mathbf{y} - μ_x) / σ_x.

### Value

`get_gamma_bounds` returns a vector of length 2 with `"lower"` and `"upper"` bounds of γ given the range of `y`.

[Package LambertW version 0.6.7 Index]