t given a specific detection system that supplies real valued scores for a trial i e a test sample and a claimed model the detection error tradeoff analysis criterion detac is formulated for two cases of score distribution types 1 the gaussian and 2 the gaussian mixture distribution as regards gaussian distributed detection scores it should be noted that the det curve generally appears as a straight line for these distributions assuming that the impostor false claims trial scores are normally distributed with mean u03bc 1 and standard deviation u03c3 1 and the true target scores with u03bc 2 and u03c3 2 the detac criterion is formulated in variants of constrained and unconstrained optimization with an optimization parameter set u03b8 as follows u03b8 arg min u03b8 u03c9 r r u03b8 u2212 c r u03c9 d d u03b8 u2212 c d 3 r u2061 u03b8 w r u2061 u03c3 1 u2061 u03b8 u03c3 2 u2061 u03b8 c r d u2061 u03b8 w d u2061 u03bc 1 u2061 u03b8 u03bc 2 u2061 u03b8 u03c3 2 u2061 u03b8 c d is the delta term corresponding to the det line as and u03c9 r u03c9 d u03b5 being arbitrary regulator constants and c r c d u03b5 the initial values of the sigma ratio and the delta term respectively the minimization 1 aims at reducing or increasing the slope of the det.