EXPRESSIONS FOR THE AREA UNDER THE CHI-SQUARE RECEIVER OPERATING CHARACTERISTIC

Many psychophysical models propose chi-square random variables for the sensory evidence. This is true for the energy-detection model when Ga ussian noise processes ate being discriminated. Parametric equations f or the chi-square receiver operating characteristic (ROC) are presente d and then the index A, equal to the area under the chi-square ROC, is determined. The index A, is shown to follow the incomplete beta distr ibution with parameters a=b=v/2 and x=1/(k+1), where k=sigma(n)(2)/sig ma(sn)(2) and v is the number of degrees of freedom of the noise proce ss.