Both families add a shape parameter to the normal distribution.

When the shape parameter is zero, the normal distribution results.

Similarly, one can calculate the value of shape parameters required for the geometric mean to equal 1/2.

The log geometric variances are positive for all values of the shape parameters.

If one of the shape parameters is known, the problem is considerably simplified.

For small values of the shape parameter, the algorithms are often not valid.

However, distributional families can have radically different shapes depending on the value of the shape parameter.

Therefore, finding a reasonable choice for the shape parameter is a necessary step in the analysis.

These correlation coefficients are plotted against their corresponding shape parameters.

How sensitive is the choice of the shape parameter?