get_support function

Computes support for skewed Lambert W x F distributions

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 $[a,b]$, c("$a,b \\in R \\cup \\pm\n$", "$\\infty$") depending on $\boldsymbol \beta$ and (the sign of) $\gamma$.

For scale-families no truncation occurs.

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".

Returns

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

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))