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

Abstract

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).

Electrophysiological correlates of face and object perception: A comparative analysis of 2D laboratory and virtual reality conditions

“…Given the frequent interest in identifying differences in locations and scales in EEG signals, the utilization of median analysis, such as the determination of median peak‐amplitude latencies (see Figure S1) or the calculation of coefficients of variance (Ospina & Marmolejo‐Ramos, 2019), proves highly advantageous. Furthermore, the exploration of alternative techniques, including robust statistics and distributional regression (Klein, 2024), warrants consideration as alternatives to conventional parametric statistical methods like anova s. Additionally, representing data in a manner congruent with its underlying distributional characteristics enables more comprehensive data exploration (e.g., cumulative distribution function plots; Marmolejo‐Ramos et al., 2023) (see Figure S2).…”

Beta transformation of the Exponential-Gaussian distribution with its properties and applications

“…The exponential-Gaussian (Ex-Gaussian), also called the exponentially modified Gaussian (EMG) distribution, is a probability distribution that convolutions exponential and normal random variables and is used in signal processing, finance, and neuroscience for skewness and heavy tails data. It has a closed-form probability density function and a cumulative distribution function, making it useful for statistical analysis [36][37][38][39]. For ∀µ ∈ R, σ , λ > 0, and ∀x ∈ R, its PDF, CDF, Hazard, and Survival functions are given in the Equations (1)(2)(3)(4), respectively.…”

“…In the scenario where α = β = 1 and λ → ∞, the BExG distribution Equation ( 10) transforms into the Gaussian distribution. This transformation is described by the parameters µ and σ proposed by the study mentioned in Marmolejo-Ramos et al [37].…”

“…In the case where β = 1, λ → ∞, and α = 1, the BExG distribution Equation ( 6) conforms to the power-normal distribution. This distribution is characterized by parameters µ, σ , and α, as studied by Chen et al [42] and Marmolejo-Ramos et al [37].…”

“…When β = 1, the BExG distribution Equation (3.2) reduces to the generalized exponential-Gaussian distribution. This reduction is governed by parameters λ, µ, σ , and α according to the study mentioned in Marmolejo-Ramos et al [37]. 4.…”