a numeric vector of real values (the observed data).

character; name of input distribution; see get_distnames.

type of Lambert W \times F distribution: skewed "s"; heavy-tail "h"; or skewed heavy-tail "hh".

list; a (possibly incomplete) list of parameters alpha, beta, gamma, delta. complete_theta fills in default values for missing entries.

numeric vector (deprecated); parameter \boldsymbol β of the input distribution. See check_beta on how to specify beta for each distribution.

scalar (deprecated); skewness parameter; default: 0.

scalar or vector (length 2) (deprecated); heavy-tail parameter(s); default: 0.

scalar or vector (length 2) (deprecated); heavy tail exponent(s); default: 1.

named vector τ which defines the variable transformation. Must have at least 'mu_x' and 'sigma_x' element; see complete_tau for details.

logical; if TRUE, it returns the standardized input that corresponds to U, which is the zero-mean and/or unit-variance version of input X \sim F_X.

logical; if TRUE it uses mean and variance implied by \boldsymbol β to do the transformation (Goerg 2011). If FALSE, it uses the alternative definition from Goerg (2016) with location and scale parameter.