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

Measurements of response inhibition components of reactive inhibition and proactive inhibition within the stop signal paradigm have been of special interest for researchers since the 1980s. While frequentist nonparametric and Bayesian parametric methods have been proposed to precisely estimate the entire distribution of reactive inhibition, quantified by stop signal reaction times(SSRT), there is no method yet in the stop-signal task literature to precisely estimate the entire distribution of proactive inhibition. We introduce an Asymmetric Laplace Gaussian (ALG) model to describe the distribution of proactive inhibition. The proposed method is based on two assumptions of independent trial type(go/stop) reaction times, and Ex-Gaussian (ExG) models for them. Results indicated that the four parametric, ALG model uniquely describes the proactive inhibition distribution and its key shape features; and, its hazard function is monotonically increasing as are its three parametric ExG components. In conclusion, both response inhibition components can be uniquely modeled via variations of the four parametric ALG model described with their associated similar distributional features.