  The area under the ROC curve is widely used as a measure of performance of
classification rules. However, it has recently been shown that the measure is
fundamentally incoherent, in the sense that it treats the relative severities
of misclassifications differently when different classifiers are used. To
overcome this, Hand (2009) proposed the $H$ measure, which allows a given
researcher to fix the distribution of relative severities to a
classifier-independent setting on a given problem. This note extends the
discussion, and proposes a modified standard distribution for the $H$ measure,
which better matches the requirements of researchers, in particular those faced
with heavily unbalanced datasets, the $Beta(\pi_1+1,\pi_0+1)$ distribution.
[Preprint submitted at Pattern Recognition Letters]
