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

Fernando Marmolejo-Ramos; Carlos Barrera-Causil; Shenbing Kuang; Zeinab Fazlali; Detlef Wegener; Thomas Kneib; Fernanda De Bastiani; Guillermo Martinez-Flórez

doi:10.1007/s11571-022-09813-2

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

Cogn Neurodyn. 2023 Feb;17(1):221-237. doi: 10.1007/s11571-022-09813-2. Epub 2022 May 17.

Authors

Fernando Marmolejo-Ramos¹, Carlos Barrera-Causil², Shenbing Kuang³, Zeinab Fazlali^{4

5}, Detlef Wegener⁶, Thomas Kneib⁷, Fernanda De Bastiani⁸, Guillermo Martinez-Flórez^{9

10}

Affiliations

¹ Centre for Change and Complexity in Learning, University of South Australia, Adelaide, 5000 Australia.
² Facultad de Ciencias Exactas y Aplicadas, Instituto Tecnológico Metropolitano -ITM, Medellín, 050034 Colombia.
³ Institute of Psychology, Chinese Academy of Sciences, Beijing, 100101 China.
⁴ School of Cognitive Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran.
⁵ Department of Psychiatry, Division of Integrative Neuroscience, Columbia University and the New York State Psychiatric Institute, New York, USA.
⁶ Brain Research Institute, Center for Cognitive Science, University of Bremen, Bremen, Germany.
⁷ Campus Institute Data Science (CIDAS) and Chair of Statistics, Georg-August-Universität Göttingen, Göttingen, Germany.
⁸ Statistics Department, Federal University of Pernambuco, Recife, Pernambuco Brazil.
⁹ Departamento de Matemáticas y Estadística, Facultad de Ciencias, Universidad de Córdoba, Córdoba, 2300 Colombia.
¹⁰ Programa de Pós-Graduação em Modelagem e Métodos Quantitativos, Universidade Federal do Ceará, Fortaleza, Brazil.

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).

Keywords: Cognitive neuroscience; Exponential Gaussian distribution; Generalised additive models for location, Scale and shape; Neuronal response latency; Reaction times.