The Folded Power Transformation
The folded power transformation is defined as
![\[ \mbox{f}(y;\lambda ) = \left\{ \begin{array}{l l} \frac{y^\lambda - (1-y)^\lambda }{\lambda } & \mbox{if } \lambda \neq 0 \\ \log (p) & \mbox{if } \lambda = 0 \end{array} \right. \]](images/imlsug_ugvartransform0045.png){kind=small} |
The normalized folded power transformation is defined as (Atkinson, 1985, p. 139)
![\[ \bm {z}_{\mbox{\tiny f}}(\lambda ; y) = \left\{ \begin{array}{l l} \frac{y^{\lambda } - (1-y)^{\lambda }}{\lambda G_{\mbox{\tiny f}}(\lambda )} & \mbox{if } \lambda \neq 0 \\ \log (p) G(y(1-y)) & \mbox{if } \lambda = 0 \end{array} \right. \]](images/imlsug_ugvartransform0046.png){kind=small} |
where 
. When you select the folded power transformation, a plot of 
appears. You should choose a value close to the MLE value.