Most models of auditory nerve response to electrical stimulation are deterministic, despite significant physiological evidence for stochastic activity. Furthermore, psychophysical models and analyses of physiological data using deterministic descriptions do not accurately predict many psychophysical phenomena. In this paper we investigate whether inclusion of stochastic activity in neural models improves such predictions. To avoid the complication of interpulse interactions and to enable the use of a simpler and faster auditory nerve model we restrict our investigation to single pulses and low-rate (< 200 pulses/s) pulse trains. We apply signal detection theory to produce direct predictions of behavioral threshold, dynamic range and intensity difference limen. Specifically, we investigate threshold versus pulse duration (the strength-duration characteristics), threshold and uncomfortable loudness (and the corresponding dynamic range) versus phase duration, the effects of electrode configuration on dynamic range and on strength-duration, threshold versus number of pulses (the temporal-integration characteristics), intensity difference limen as a function of loudness, and the effects of neural survival on these measures. For all psychophysical measures investigated, the inclusion of stochastic activity in the auditory nerve model was found to produce more accurate predictions.