R: Utilities for transformation vector tau

tau-utils {LambertW} | R Documentation

## Utilities for transformation vector tau

### Description

All functions here are for the transformation parameter vector τ = (μ_x, σ_x, γ, δ, α).

`check_tau` checks if τ is correctly specified (correct names, non-negativity constraints, etc.)

`complete_tau` completes missing values so users don't have to specify every element of τ 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 τ.

`normalize_by_tau` shifts and scales data given the `tau` vector as

(data - μ_x) / σ_x.

Parameters μ_x and σ_x are not necessarily mean and standard deviation in the τ 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 τ to the parameter list θ (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)

### Arguments

`tau` | named vector τ 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 σ_x + μ_x
`beta` | numeric vector (deprecated); parameter \boldsymbol β of the input distribution. See `check_beta` on how to specify `beta` for each distribution.

### Value

`check_tau` throws an error if τ 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"`.

[Package LambertW version 0.6.7 Index]