Box-Cox Transformation

boxCox() applies the Box-Cox transformation to a numeric vector.
boxCoxInv() reverses the transformation.

Usage

boxCox(x, lambda, tol = 0.000001)

boxCoxInv(x, lambda, tol = 0.000001)

Arguments

x: a numeric vector. Must contain strictly positive values (except NAs).
lambda: a single numeric transformation parameter
tol: numeric tolerance for detecting the special case $\lambda \approx 0$

Value

a numeric vector of the same length as x. An input consisting only of NA is an error.

Details

The Box-Cox transformation is defined for strictly positive values of x and is given by

$$ f_\lambda(x) = \left\{ \begin{array}{ll} (x^\lambda - 1) / \lambda & \mbox{if } \lambda \neq 0 \\ \log(x) & \mbox{if } \lambda = 0 \end{array} \right. $$

The transformation requires strictly positive input values. If |lambda| < tol, the logarithmic transformation is used instead for numerical stability.

The inverse transformation recovers the original data (up to numerical precision) when the same lambda and tol are used.

References

Box, G. E. P. and Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society, Series B, 26(2), 211–252.

Examples

set.seed(1)
x <- rlnorm(500, 1, 0.5)

y <- boxCox(x, lambda = 0.5)
xBack <- boxCoxInv(y, lambda = 0.5)

# check inversion
max(abs(x - xBack))
#> [1] 1.776357e-15

# log-transform (lambda ~ 0)
y0 <- boxCox(x, lambda = 0)