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