tau-utils: Utilities for transformation vector tau

Description

All functions here are for the transformation parameter vector $\tau = (\mu_x, \sigma_x, \gamma, \delta, \alpha)$.

check_tau checks if $\tau$ is correctly specified (correct names, non-negativity constraints, etc.)

complete_tau completes missing values so users don't have to specify every element of $\tau$ explicitly. 'mu_x' and 'sigma_x' must be specified, but alpha = 1, gamma = 0, and delta = 0 will be set automatically if missing.

get_initial_tau provides starting estimates for $\tau$.

normalize_by_tau shifts and scales data given the tau vector as $$(data - \mu_x) / \sigma_x.$$

Parameters $\mu_x$ and $\sigma_x$ are not necessarily mean and standard deviation in the $\tau$ vector; that depends on the family type and use.mean.variance (for location families they usually are mean and standard deviation if use.mean.variance = TRUE; for scale and non-location non-scale families they are just location/scale parameters for the transformation).

tau2theta converts $\tau$ to the parameter list $\theta$ (inverse of theta2tau).

tau2type guesses the type ('s', 'h', 'hh') from the names of tau vector; thus make sure tau is named correctly.

Usage

check_tau(tau)
complete_tau(tau, type = tau2type(tau))
get_initial_tau(y, type = c("h", "hh", "s"), location.family = TRUE)
normalize_by_tau(data, tau, inverse = FALSE)
tau2theta(tau, beta)
tau2type(tau)

Value

check_tau throws an error if $\tau$ does not define a proper transformation.

complete_tau returns a named numeric vector.

get_initial_tau returns a named numeric vector.

tau2theta returns a list with entries alpha, beta,

gamma, and delta.

tau2type returns a string: either "s", "h", or

"hh".

Arguments

tau: named vector $\tau$ which defines the variable transformation. Must have at least 'mu_x' and 'sigma_x' element; see complete_tau for details.
type: type of Lambert W $\times$ F distribution: skewed "s"; heavy-tail "h"; or skewed heavy-tail "hh".
y: a numeric vector of real values (the observed data).
location.family: logical; if FALSE it sets mu_x to 0 and only estimates sigma_x; if TRUE (default), it estimates mu_x as well.
data: numeric; a numeric object in R. Usually this is either y or x (or z and u if inverse = TRUE.)
inverse: logical; if TRUE it applies the inverse transformation $data \cdot \sigma_x + \mu_x$
beta: numeric vector (deprecated); parameter $\boldsymbol \beta$ of the input distribution. See check_beta on how to specify beta for each distribution.