LambertW (version 0.6.9-1)

get_support: 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))

Value

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

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).

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))