get_support {LambertW}

Computes support for skewed Lambert W x F distributions

Description

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

For scale-families no truncation occurs.

Usage

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

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.

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 \gamma \neq 0) for input with support on the entire real line. For \gamma = 0 the support of Y is the same as for X. Heavy-tail Lambert W RVs are not affected by truncated support (for \delta \geq 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))