We have also discussed cost weighting in the context of ROC, and Hand (2009) seeks to improve on ROC AUC by introducing a beta distribution as an estimated cost profile, but we will not discuss them further here as we are more interested in the effectiveness of the classifer overall rather than matching a particular cost profile, and are skeptical about any generic cost distribution.
the beta distribution gives priority to central tendency rather than boundary conditions, but boundary conditions are frequently encountered in optimization.