get_input function

Back-transform Y to X

get_input back-transforms the observed data $\boldsymbol y$ to the (approximate) input data $\boldsymbol x_{\tau}$ using the transformation vector c("$\\tau = (\\mu_x(\\boldsymbol \\beta),\n$", "$\\sigma_x(\\boldsymbol \\beta), \\gamma, \\alpha, \\delta)$").

Note that get.input should be deprecated; however, since it was explicitly referenced in Goerg (2011) I keep it here for future reference. New code should use get_input exclusively.

get_input(y, tau, return.u = FALSE)

get.input(...)

Arguments

• y: a numeric vector of data values or an object of class LambertW_fit.
• tau: named vector $\tau$ which defines the variable transformation. Must have at least 'mu_x' and 'sigma_x' element; see complete_tau for details.
• return.u: should the normalized input be returned; default: FALSE.
• ...: arguments passed to get_input.

Returns

The (approximated) input data vector c("\\widehat{\\boldsymbol\n", "x}_{\\tau}").

For gamma != 0 it uses the principal branch solution W_gamma(z, branch = 0) to get a unique input.

For gamma = 0 the back-transformation is bijective (for any $\delta \geq 0, \alpha \geq 0$).

If return.u = TRUE, then it returns a list with 2 vectors - u: centered and normalized input $\widehat{\boldsymbol u}_{\theta}$,

• x: input data $\widehat{\boldsymbol x}_{\theta}$.

Examples

set.seed(12)
# unskew very skewed data
y <- rLambertW(n = 1000, theta = list(beta = c(0, 1), gamma = 0.3), 
               distname = "normal")
test_normality(y)
fit.gmm <- IGMM(y, type="s")

x <- get_input(y, fit.gmm$tau)
# the same as
x <- get_input(fit.gmm)
test_normality(x) # symmetric Gaussian

See Also

get_output