R: Back-transform Y to X

get_input {LambertW}

R Documentation

Back-transform Y to X

Description

get_input back-transforms the observed data \boldsymbol y to the (approximate) input data \boldsymbol x_{τ} using the transformation vector τ = (μ_x(\boldsymbol β), σ_x(\boldsymbol β), γ, α, δ).

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.

Usage

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 τ 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`.

Value

The (approximated) input data vector \widehat{\boldsymbol x}_{τ}.

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 δ ≥q 0, α ≥q 0).

If return.u = TRUE, then it returns a list with 2 vectors

`u`	centered and normalized input \widehat{\boldsymbol u}_{θ},
`x`	input data \widehat{\boldsymbol x}_{θ}.

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