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.

[1]  R. Hohle.  INFERRED COMPONENTS OF REACTION TIMES AS FUNCTIONS OF FOREPERIOD DURATION. , 1965, Journal of experimental psychology.

[2]  Skew-normal alpha-power model , 2014 .

[3]  Heleno Bolfarine,et al.  Flexible Birnbaum-Saunders Distribution , 2019, Symmetry.

[4]  M. Genton,et al.  Flexible Class of Skew‐Symmetric Distributions , 2004 .

[5]  A. Azzalini,et al.  Statistical applications of the multivariate skew normal distribution , 2009, 0911.2093.

[6]  C. Drossaert,et al.  Validation of the Flourishing Scale in a sample of people with suboptimal levels of mental well-being , 2016, BMC Psychology.

[7]  A. Azzalini.  A class of distributions which includes the normal ones , 1985 .

[8]  H. Akaike.  A new look at the statistical model identification , 1974 .

[9]  E. Grushka.  Characterization of exponentially modified Gaussian peaks in chromatography. , 1972, Analytical chemistry.

[10]  Fernando Marmolejo-Ramos,et al.  Modeling neural activity with cumulative damage distributions , 2015, Biological Cybernetics.

[11]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[12]  R. Luce,et al.  Decision structure and time relations in simple choice behavior , 1956 .

[13]  Likelihood-based inference for power distributions , 2012 .

[14]  Fernando Marmolejo-Ramos,et al.  Theoretical models of reaction times arising from simple-choice tasks , 2019, Cognitive Neurodynamics.

[15]  Yuri A. Iriarte,et al.  A Gamma-Type Distribution with Applications , 2020, Symmetry.

[16]  P. König,et al.  Testing the theory of embodied cognition with subliminal words , 2010, Cognition.

[17]  S. Rocky Durrans,et al.  Distributions of fractional order statistics in hydrology , 1992 .

[18]  Fernando Marmolejo-Ramos,et al.  Fatigue-life distributions for reaction time data , 2018, Cognitive Neurodynamics.

[19]  J. Robins,et al.  Likelihood-based inference with singular information matrix , 2000 .