Fatigue-life distributions for reaction time data

Generalised exponential-Gaussian distribution: a method for neural reaction time analysis

Reaction times (RTs) are an essential metric used for understanding the link between brain and behaviour. As research is reaffirming the tight coupling between neuronal and behavioural RTs, thorough statistical modelling of RT data is thus essential to enrich current theories and motivate novel findings. A statistical distribution is proposed herein that is able to model the complete RT's distribution, including location, scale and shape: the generalised-exponential-Gaussian (GEG) distribution. The GEG distribution enables shifting the attention from traditional means and standard deviations to the entire RT distribution. The mathematical properties of the GEG distribution are presented and investigated via simulations. Additionally, the GEG distribution is featured via four real-life data sets. Finally, we discuss how the proposed distribution can be used for regression analyses via generalised additive models for location, scale and shape (GAMLSS).

The Exponential-Centred Skew-Normal Distribution

Data from some research fields tend to exhibit a positive skew. For example, in experimental psychology, reaction times (RTs) are characterised as being positively skewed. However, it is not unlikely that RTs can take a normal or, even, a negative shape. While the Ex-Gaussian distribution is suitable to model positively skewed data, it cannot cope with negatively skewed data. This manuscript proposes a distribution that can deal with both negative and positive skews: the exponential-centred skew-normal (ECSN) distribution. The mathematical properties of the proposed distribution are reported, and it is featured in two non-synthetic datasets.

Theoretical models of reaction times arising from simple-choice tasks

In this work we present a group of theoretical models for reaction times arising from simple-choice task tests. In particular, we argue for the inclusion of a shifted version of the Gamma distribution as a theoretical model based on a mathematical result on first hitting times. We contrast the goodness-of-fit of those models with the Ex-Gaussian distribution, using data from recently published experiments. The evidence of the results obtained highlights the convenience of proposing theoretical models for reaction times instead of models acting exclusively as quantitative distribution measurements.