scholarly journals The Exponential-Centred Skew-Normal Distribution

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1140
Author(s):  
Guillermo Martínez-Flórez ◽  
Carlos Barrera-Causil ◽  
Fernando Marmolejo-Ramos
Keyword(s):  
Normal Distribution ◽  
Gaussian Distribution ◽  
Experimental Psychology ◽  
Reaction Times ◽  
Skewed Data ◽  
Skew Normal Distribution ◽  
Research Fields ◽  
Mathematical Properties ◽  
Synthetic Datasets ◽  
Skew Normal

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.

scholarly journals Some properties of the unified skew-normal distribution

2021 ◽  
Author(s):  
Reinaldo B. Arellano-Valle ◽  
Adelchi Azzalini
Keyword(s):  
Normal Distribution ◽  
Fourth Order ◽  
Probability Distributions ◽  
Skew Normal Distribution ◽  
Present Contribution ◽  
The Family ◽  
Multivariate Skewness ◽  
Unified Skew Normal Distribution ◽  
Skewness And Kurtosis ◽  
Skew Normal

AbstractFor the family of multivariate probability distributions variously denoted as unified skew-normal, closed skew-normal and other names, a number of properties are already known, but many others are not, even some basic ones. The present contribution aims at filling some of the missing gaps. Specifically, the moments up to the fourth order are obtained, and from here the expressions of the Mardia’s measures of multivariate skewness and kurtosis. Other results concern the property of log-concavity of the distribution, closure with respect to conditioning on intervals, and a possible alternative parameterization.

scholarly journals Copulaesque Versions of the Skew-Normal and Skew-Student Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 815
Author(s):  
Christopher Adcock
Keyword(s):  
Distribution Function ◽  
Normal Distribution ◽  
Degrees Of Freedom ◽  
Special Functions ◽  
Normal Distribution Function ◽  
Skew Normal Distribution ◽  
Marginal Distributions ◽  
Student’S T ◽  
Normal Copula ◽  
Skew Normal

A recent paper presents an extension of the skew-normal distribution which is a copula. Under this model, the standardized marginal distributions are standard normal. The copula itself depends on the familiar skewing construction based on the normal distribution function. This paper is concerned with two topics. First, the paper presents a number of extensions of the skew-normal copula. Notably these include a case in which the standardized marginal distributions are Student’s t, with different degrees of freedom allowed for each margin. In this case the skewing function need not be the distribution function for Student’s t, but can depend on certain of the special functions. Secondly, several multivariate versions of the skew-normal copula model are presented. The paper contains several illustrative examples.

The additive logistic skew-normal distribution on the simplex

2005 ◽  
Vol 19 (3) ◽  
pp. 205-214 ◽  
Author(s):  
G. Mateu-Figueras ◽  
V. Pawlowsky-Glahn ◽  
C. Barceló-Vidal
Keyword(s):  
Normal Distribution ◽  
Skew Normal Distribution ◽  
Skew Normal
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