Apply / invert a Box-Cox power transformation

The Box-Cox transformation (Box & Cox, 1964) is $$y(\lambda) = \begin{cases} (x^\lambda - 1) / \lambda & \lambda \neq 0 \\ \log(x) & \lambda = 0. \end{cases}$$

Usage

box_cox(x, lambda)

Arguments

x

Numeric vector of strictly positive values.

lambda

Numeric scalar. Power parameter.

Value

A numeric vector of transformed values.

Details

For lambda = 0 this returns log(x); for lambda = 1 it returns x - 1 (no shape change). Use shewhart_box_cox() to estimate lambda from the data via profile log-likelihood.

References

Box, G. E. P., & Cox, D. R. (1964). An Analysis of Transformations. Journal of the Royal Statistical Society, Series B, 26(2), 211-252. doi:10.1111/j.2517-6161.1964.tb00553.x

See also

shewhart_box_cox() to estimate lambda from data.

Examples

box_cox(1:10, lambda = 0)      # equivalent to log(1:10)
#>  [1] 0.0000000 0.6931472 1.0986123 1.3862944 1.6094379 1.7917595 1.9459101
#>  [8] 2.0794415 2.1972246 2.3025851
box_cox(1:10, lambda = 0.5)
#>  [1] 0.0000000 0.8284271 1.4641016 2.0000000 2.4721360 2.8989795 3.2915026
#>  [8] 3.6568542 4.0000000 4.3245553