Fatigue-life distributions for reaction time data

Abstract

The family of fatigue-life distributions is introduced as an alternative model of reaction time data. This family includes the shifted Wald distribution and a shifted version of the Birnbaum-Saunders distribution. Although the former has been proposed as a way to model reaction time data, the latter has not. Hence, we provide theoretical, mathematical and practical arguments in support of the shifted Birnbaum-Saunders as a suitable model of simple reaction times and associated cognitive mechanisms.

The Exponential-Centred Skew-Normal Distribution

“…For Z ∼ SN(α), with E(Z) = bδ and Var(Z) = 1 − (bδ) 2 where b = 2 π and δ = α √ 1+α 2 , let the Y random variable be defined as:…”

“…Other distributions, though, have been proposed to model RT data. For example, it has been shown that the shifted Wald, shifted Birnbaum-Saunders [2] and shifted Gamma distributions [3] provide good fits to RT data (the Birnbaum-Saunders distribution has also been used to model neural activity [4], and a flexible version of it was proposed recently [5]. The slashed quasi-Gamma distribution (an extension of the generalised Gamma distribution) has been proposed to model data with varying skewness and high kurtosis [6].…”

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

“…For example, Tejo et al. ( 2018 , 2019 ), and Martínez-Flórez et al. ( 2020 ) have put forward the shifted Birnbaum–Saunders, shifted Gamma distributions, and Exponential-Centred Skew-Normal distributions, respectively, as good fits to RTs.…”

The place of probability distributions in statistical learning. A commented book review of ‘Distributions for modeling location, scale, and shape using GAMLSS in R’ by Rigby et al. (2021)

“…There are distributions that do not follow a Gaussian shape and are also present in statistics. For example, the Negative Binomial, Log-Normal, and Gamma distributions have been featured in statistical models used to inform COVID-related policies (e.g., in South Australia's COVIDready plan), the Ex-Gaussian, Inverse Gaussian (aka Wald), and Birnbaum-Saunders distributions have been used to model human reaction times (Tejo et al 2019;Tejo, Niklitschek-Soto & Marmolejo-Ramos 2018;Leiva et al 2015), and the Skew-Normal distribution has been used for proposing a new form of linear mixed model (Schumacher, Lachos & Matos 2021). But the ubiquity of probability distributions does not stop there.…”