The Guerrero-Johnson Transformation
The Guerrero-Johnson transformation is defined as
![\[ \mbox{GJ}(y;\lambda ) = \left\{ \begin{array}{l l} \frac{p^\lambda - 1}{\lambda } & \mbox{if } \lambda \neq 0 \\ \log (p) & \mbox{if } \lambda = 0 \end{array} \right. \]](images/imlsug_ugvartransform0049.png){kind=small} |
The normalized Guerrero-Johnson transformation is defined as (Atkinson, 1985, p. 145)
![\[ \bm {z}_{\mbox{\tiny GJ}}(\lambda ; y) = \left\{ \begin{array}{l l} \frac{p^{\lambda } - 1}{\lambda G_{\mbox{\tiny GJ}}(\lambda )} & \mbox{if } \lambda \neq 0 \\ \log (p) G(y(1-y)) & \mbox{if } \lambda = 0 \end{array} \right. \]](images/imlsug_ugvartransform0050.png){kind=small} |
where 
. When you select the Guerrero-Johnson transformation, a plot of 
appears. You should choose a value close to the MLE value.