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.
get_gamma_bounds(y, tau)get_gamma_bounds returns a vector of length 2 with
"lower" and "upper" bounds of \(\gamma\) given the range
of y.
a numeric vector of real values (the observed data).
named vector \(\tau\) which defines the variable transformation.
Must have at least 'mu_x' and 'sigma_x' element; see
complete_tau for 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 \(\mathbf{z} = (\mathbf{y} -
\mu_x) / \sigma_x\).