lambert: Lambert W x F Normalization

In bestNormalize: Normalizing Transformation Functions

Lambert W x F Normalization

Description

Perform Lambert's W x F transformation and center/scale a vector to attempt normalization via the LambertW package.

Usage

lambert(x, type = "s", standardize = TRUE, warn = FALSE, ...)

## S3 method for class 'lambert'
predict(object, newdata = NULL, inverse = FALSE, ...)

## S3 method for class 'lambert'
print(x, ...)

Arguments

x	A vector to normalize with Box-Cox
type	a character indicating which transformation to perform (options are "s", "h", and "hh", see details)
standardize	If TRUE, the transformed values are also centered and scaled, such that the transformation attempts a standard normal
warn	should the function show warnings
...	Additional arguments that can be passed to the LambertW::Gaussianize function
object	an object of class 'lambert'
newdata	a vector of data to be (reverse) transformed
inverse	if TRUE, performs reverse transformation

Details

lambert uses the LambertW package to estimate a normalizing (or "Gaussianizing") transformation. This transformation can be performed on new data, and inverted, via the predict function.

NOTE: The type = "s" argument is the only one that does the 1-1 transform consistently, and so it is the only method currently used in bestNormalize(). Use type = "h" or type = 'hh' at risk of not having this estimate 1-1 transform. These alternative types are effective when the data has exceptionally heavy tails, e.g. the Cauchy distribution.

Additionally, sometimes (depending on the distribution) this method will be unable to extrapolate beyond the observed bounds. In these cases, NaN is returned.

Value

A list of class lambert with elements

x.t	transformed original data
x	original data
mean	mean after transformation but prior to standardization
sd	sd after transformation but prior to standardization
tau.mat	estimated parameters of LambertW::Gaussianize
n	number of nonmissing observations
norm_stat	Pearson's P / degrees of freedom
standardize	was the transformation standardized

The predict function returns the numeric value of the transformation performed on new data, and allows for the inverse transformation as well.

References

Georg M. Goerg (2016). LambertW: An R package for Lambert W x F Random Variables. R package version 0.6.4.

Georg M. Goerg (2011): Lambert W random variables - a new family of generalized skewed distributions with applications to risk estimation. Annals of Applied Statistics 3(5). 2197-2230.

Georg M. Goerg (2014): The Lambert Way to Gaussianize heavy-tailed data with the inverse of Tukey's h transformation as a special case. The Scientific World Journal.

See Also

Gaussianize

Examples

## Not run: 
x <- rgamma(100, 1, 1)

lambert_obj <- lambert(x)
lambert_obj
p <- predict(lambert_obj)
x2 <- predict(lambert_obj, newdata = p, inverse = TRUE)

all.equal(x2, x)

## End(Not run)

bestNormalize documentation built on Aug. 18, 2023, 9:08 a.m.