Mathematical and Electrical Models of Auditory Detection

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Abstract
McGill's generalization of Marill's formula for the probability of a correct response in a two‐alternative, forced‐choice experiment is obtained from a special case of the noncentral chi‐square distribution. The present paper shows that a special case of the noncentral chi distribution is more appropriate than the noncentral chi square for monaural detection of a tonal signal in a continuous background of Gaussian noise. The special noncentral chi function fits distributions obtained from an electrical model, and yields psychometric functions appropriate both to it and to human observers. Estimates of bandwidth and of integration time derived from the distribution functions lie within the range of values often assumed from human subjects.

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