LambertW (version 0.6.4)

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 $(-\mathrm{\infty },\mathrm{\infty })$, then the skewed Lambert W $\times$ F distribution has truncated support $[a,b]$, $a,b\in R\cup \pm \mathrm{\infty }$ depending on $\mathit{\beta }$ 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".

Value

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

Details

Half-open interval on the real line (if $\gamma \ne 0$) 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 $\delta \ge 0$); thus support is c(lower = -Inf, upper = Inf).

Examples

# NOT RUN {
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))
# }