This study investigates the neural correlates underpinning response inhibition using a parametric ex-Gaussian model of stop-signal task performance, fit with hierarchical Bayesian methods, in a large healthy sample (N=156). The parametric model accounted for both stop-signal reaction time (SSRT) and trigger failure (i.e., failures to initiate the inhibition process). The returned SSRT estimate (SSRTEXG3 ) was attenuated by ≈65ms compared to traditional nonparametric SSRT estimates (SSRTint ). The amplitude and latency of the N1 and P3 event-related potential components were derived for both stop-success and stop-failure trials and compared to behavioral estimates derived from traditional (SSRTint ) and parametric (SSRTEXG3 , trigger failure) models. Both the fronto-central N1 and P3 peaked earlier and were larger for stop-success than stop-failure trials. For stop-failure trials only, N1 peak latency correlated with both SSRT estimates as well as trigger failure and temporally coincided with SSRTEXG3 , but not SSRTint . In contrast, P3 peak and onset latency were not associated with any behavioral estimates of inhibition for either trial type. While the N1 peaked earlier for stop-success than stop-failure trials, this effect was not found in poor task performers (i.e., high trigger failure/slow SSRT). These findings are consistent with attentional modulation of both the speed and reliability of the inhibition process, but not for poor performers. Together with the absence of any P3 onset latency effect, our findings suggest that attentional mechanisms are important in supporting speeded and reliable inhibition processes required in the stop-signal task.