Box Cox Transformation

In statistics, it is often a desired condition that the errors are normally distributed.

A Box-Cox transformation is used for this exact reason to transform non-normally distributed data into normally distributed data.

This is done by estimating some parameter \(\lambda\) that normalizes our variable \(y\) in the following set of equations:

\[ y_{i}^{(\lambda )}={\begin{cases}{\dfrac {y_{i}^{\lambda }-1}{\lambda }}&{\text{if }}\lambda \neq 0,\\\ln y_{i}&{\text{if }}\lambda =0,\end{cases}} \]