The Decomposition of Quadratic Forms Under Matrix Variate Skew-Normal Distribution

2020 ◽  
pp. 181-194
Author(s):  
Ziwei Ma ◽  
Tonghui Wang ◽  
Baokun Li ◽  
Xiaonan Zhu ◽  
Yuede Ma
Keyword(s):  
Normal Distribution ◽  
Quadratic Forms ◽  
Skew Normal Distribution ◽  
Skew Normal

EM algorithm using overparameterization for the multivariate skew-normal distribution

2021 ◽  
Author(s):  
Toshihiro Abe ◽  
Hironori Fujisawa ◽  
Takayuki Kawashima ◽  
Christophe Ley
Keyword(s):  
Em Algorithm ◽  
Normal Distribution ◽  
Skew Normal Distribution ◽  
Skew Normal

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

On Some Properties of the Unified Skew Normal Distribution

2013 ◽  
Vol 7 (3) ◽  
pp. 480-495 ◽  
Author(s):  
Arjun K. Gupta ◽  
Mohammad A. Aziz ◽  
Wei Ning
Keyword(s):  
Normal Distribution ◽  
Skew Normal Distribution ◽  
Unified Skew Normal Distribution ◽  
Skew Normal
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