R: Computes support for skewed Lambert W x F distributions

get_support {LambertW} | R Documentation

## Computes support for skewed Lambert W x F distributions

### Description

If the input X \sim F has support on the entire real line (-∞, ∞), then the skewed Lambert W \times F distribution has truncated support [a,b], a,b \in R \cup \pm ∞ depending on \boldsymbol β and (the sign of) γ.

For scale-families no truncation occurs.

### Usage

    get_support(tau, is.non.negative = FALSE, input.bounds = c(-Inf, Inf))

### 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.
`is.non.negative` | logical; by default it is set to `TRUE` if the distribution is not a location but a scale family.
`input.bounds` | interval; the bounds of the input distribution. If `is.non.negative = FALSE`, then it will adjust it to `c(0, Inf)`; also useful for bounded input distributions, such as `"unif"`.

### Details

Half-open interval on the real line (if γ \neq 0) for input with support on the entire real line. For γ = 0 the support of Y is the same as for X. Heavy-tail Lambert W RVs are not affected by truncated support (for δ ≥q 0); thus support is `c(lower = -Inf, upper = Inf)`.

### Value

A vector of length 2 with names `'lower'` and `'upper'`.

### Examples

    get_support(c(mu_x = 0, sigma_x = 1, gamma = 0)) # as gamma = 0
    # truncated on the left since gamma > 0
    get_support(c(mu_x = 0, sigma_x = 1, gamma = 0.1))

    # no truncation for heavy tail(s)
    get_support(c(mu_x = 0, sigma_x = 1, delta = 0.1))

[Package LambertW version 0.6.7 Index]