get_gamma_bounds {LambertW}

Get bounds for gamma

Description

get_gamma_bounds returns lower and upper bounds for \gamma, 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 \tau 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 \gamma 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 \geq -1 / \exp(1). Thus, W_gamma has real-valued solutions only for z \geq -1 / \exp(1) \gamma These lower and upper bounds are determined by minimum and maxiumum of the normalized data \mathbf{z} = (\mathbf{y} - \mu_x) / \sigma_x.

Value

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