Box-Cox power transformation

The Box-Cox power transformation is a data transformation to achieve a better normality and to stabilize the variance. In MCRA, the transformation parameter \(p\) in \((y^p - 1)/p\) is determined by maximizing the log-likelihood function

\[l(p) = -\frac{n}{s} \log \left[ \frac{1}{n} \sum_{i=1}^{n} (y_{i}^{(p)} - \overline { y^{(p)}})^2 \right] + (p-1) \sum_{i=1}^n \log y_{i}\]

where \(i\) indexes the \(n\) observations and

\[\overline { y^{(p)}} = \frac{1}{n} \sum_{i=1}^{n} y_{i}^{(p)}\]

is the average of the \(y_{i}^{(p)}\), see Box and Cox (1964).