On Linear DETs

This paper investigates the properties of a popular ROC variant - the detection error trade-off plot (DET). In particular, we derive a set of conditions on the underlying probability distributions to produce linear DET plots in a generalized setting. We show that the linear DETs on a normal deviate scale are not exclusively produced by normal distributions, however, that normal distributions do play an unique role in the threshold behavior as one moves along the DET line. An interesting connection between linear DETs and the Kullback-Leibler divergence is also discussed.