An increment threshold law for stimuli of arbitrary statistics

We obtain a generalized increment threshold law that describes the relationship between the just detectable average signal increment and the noise when the threshold is stabilized, for the usual yes-no (nonorthogonal) signal format. The results are applicable to audition and vision, for arbitrary (discrete or continuous) signal and noise statistics, and arbitrary detection probabilities. The results are most useful when the noise and signal-plusnoise probability densities have the same form. Previous treatments of this problem have been restricted to Gaussian and Poisson signal and noise densities.