We considered starts for transformations informally to ensure that all data values are positive and that the ratio of the largest to the smallest data values is sufficiently large. An alternative is...

We considered starts for transformations informally to ensure that all data values are positive and that the ratio of the largest to the smallest data values is sufficiently large. An alternative is to think of the start as a parameter to be estimated along with the transformation power to make the distribution of the variable as normal as possible. This approach defines a two-parameter Box-Cox family:

(a) Develop the MLEs of α and λ for the two-parameter Box-Cox family.

(b) Attempt to apply the estimator to data. Do you encounter any obstacles? [Hint: Examine the correlation between the parameter estimates α and λ.]