The Aranda-Ordaz Transformation
The Aranda-Ordaz transformation is defined as
![\[ \mbox{AO}(y;\lambda ) = \left\{ \begin{array}{l l} \frac{2 (p^\lambda - 1)}{\lambda (p^\lambda +1)} & \mbox{if } \lambda \neq 0 \\ \log (p) & \mbox{if } \lambda = 0 \end{array} \right. \]](images/imlsug_ugvartransform0053.png){kind=small} |
The normalized Aranda-Ordaz transformation is defined as (Atkinson, 1985, p. 149)
![\[ \bm {z}_{\mbox{\tiny AO}}(\lambda ; y) = \left\{ \begin{array}{l l} \frac{p^\lambda - 1}{\lambda (p^\lambda +1) G_{\mbox{\tiny AO}}(\lambda )} & \mbox{if } \lambda \neq 0 \\ \log (p) G(y(1-y)) & \mbox{if } \lambda = 0 \end{array} \right. \]](images/imlsug_ugvartransform0054.png){kind=small} |
where 
. When you select the Aranda-Ordaz transformation, a plot of 
appears. You should choose a value close to the MLE value.