# get_input: Back-transform Y to X In LambertW: Probabilistic Models to Analyze and Gaussianize Heavy-Tailed, Skewed Data

 get_input 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}.

get_output

### 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



LambertW documentation built on Sept. 22, 2022, 5:07 p.m.