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Measurements of response inhibition components of reactive inhibition andproactive inhibition within the stop signal paradigm have been of specialinterest for researchers since the 1980s. While frequentist nonparametric andBayesian parametric methods have been proposed to precisely estimate the entiredistribution of reactive inhibition, quantified by stop signal reactiontimes(SSRT), there is no method yet in the stop-signal task literature toprecisely estimate the entire distribution of proactive inhibition. Weintroduce an Asymmetric Laplace Gaussian (ALG) model to describe thedistribution of proactive inhibition. The proposed method is based on twoassumptions of independent trial type(go/stop) reaction times, and Ex-Gaussian(ExG) models for them. Results indicated that the four parametric, ALG modeluniquely describes the proactive inhibition distribution and its key shapefeatures; and, its hazard function is monotonically increasing as are its threeparametric ExG components. In conclusion, both response inhibition componentscan be uniquely modeled via variations of the four parametric ALG modeldescribed with their associated similar distributional features.

The AL-Gaussian Distribution as the Descriptive Model for the Internal Proactive Inhibition in the Standard Stop Signal Task