Some skew-symmetric models

Gupta, Arjun K.; Chang, Fu; Huang, Wen-Jang

doi:10.1515/rose.2002.10.2.133

Cited by 112 publications

(62 citation statements)

References 8 publications

(6 reference statements)

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“…An attractive class of Skew-Symmetric (SS) distributions defined in terms of the pdf appears in Azzalini [20], Azzalini and Capitanio [21] and Gupta et al [22]:…”

Section: Generalized Skew-normal Distributionsmentioning

confidence: 99%

Generalized Skew-Normal Negentropy and Its Application to Fish Condition Factor Time Series

Arellano–Valle

Contreras-Reyes

Stehlík

2017

Entropy

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Abstract:The problem of measuring the disparity of a particular probability density function from a normal one has been addressed in several recent studies. The most used technique to deal with the problem has been exact expressions using information measures over particular distributions. In this paper, we consider a class of asymmetric distributions with a normal kernel, called Generalized Skew-Normal (GSN) distributions. We measure the degrees of disparity of these distributions from the normal distribution by using exact expressions for the GSN negentropy in terms of cumulants. Specifically, we focus on skew-normal and modified skew-normal distributions. Then, we establish the Kullback-Leibler divergences between each GSN distribution and the normal one in terms of their negentropies to develop hypothesis testing for normality. Finally, we apply this result to condition factor time series of anchovies off northern Chile.

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“…An attractive class of Skew-Symmetric (SS) distributions defined in terms of the pdf appears in Azzalini [20], Azzalini and Capitanio [21] and Gupta et al [22]:…”

Section: Generalized Skew-normal Distributionsmentioning

confidence: 99%

Generalized Skew-Normal Negentropy and Its Application to Fish Condition Factor Time Series

Arellano–Valle

Contreras-Reyes

Stehlík

2017

Entropy

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“…By doing so, we will obtain more robust estimators for the parameters of the mixture regression model. We will use the Azzalini type skew t distribution (Azzalini and Capitanio 2003, Gupta et al 2002, Gupta 2003 with the following density function…”

Section: Robust Mixture Regression Based On the Skew T Distributionmentioning

confidence: 99%

“…This is an extension of the mixture of skew t distribution proposed by Lin et al (2007) to the mixture regression models. We will use the skew t distribution results from the scale mixture of the skew normal distribution introduced by Gupta et al (2002), Gupta (2003) and Azzalini and Capitaino (2003). The scale mixture representation of the skew t distribution enables to easily implement an EM algorithm to obtain the ML estimates for the parameters of interest in the mixture regression model.…”

Section: Introductionmentioning

confidence: 99%

Robust mixture regression based on the skew t distribution

Doğru

Arslan

2017

Rev. colomb. estad.

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In this study, we propose a robust mixture regression procedure based on the skew t distribution to model heavy-tailed and/or skewed errors in a mixture regression setting. Using the scale mixture representation of the skew t distribution, we give an Expectation Maximization (EM) algorithm to compute the maximum likelihood (ML) estimates for the paramaters of interest. The performance of proposed estimators is demonstrated by a simulation study and a real data example.

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“…Henze (1986) obtained a stochastic representation for the SN and used it to obtain its odd moments. A comprehensive treatment of the skew normal family of distributions can be found in Genton (2004), Arellano-Valle et al (2004, 2005 and Gupta et al (2002).…”

Section: Introductionmentioning

confidence: 99%

The Continuous Hidden Threshold Mixed Skew-Symmetric Distribution

Bouaddi

Belhachemi²,

Douch³

2015

SSRN Journal

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This paper explores a way to construct a new family of univariate probability distributions where the parameters of the distribution capture the dependence between the variable of interest and the continuous latent state variable (the regime). The distribution nests two well known families of distributions, namely, the skew normal family of Azzalini (1985) and a mixture of two Arnold et al. (1993) distribution. We provide a stochastic representation of the distribution which enables the user to easily simulate the data from the underlying distribution using generated uniform and normal variates. We also derive the moment generating function and the moments. The distribution comprises eight free parameters that make it very flexible. This flexibility allows the user to capture many stylized facts about the data such as the regime dependence, the asymmetry and fat tails as well as thin tails.

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Some skew-symmetric models

Abstract: In this paper, the classes of Symmetrie density functions which depend on a skewness Parameter have been studied. In particular the skew normal, uniform, t, Cauchy, Laplace, and logistic distributions are given and some of their properties are explored.

Cited by 112 publications

References 8 publications

Generalized Skew-Normal Negentropy and Its Application to Fish Condition Factor Time Series

Generalized Skew-Normal Negentropy and Its Application to Fish Condition Factor Time Series

Robust mixture regression based on the skew t distribution

The Continuous Hidden Threshold Mixed Skew-Symmetric Distribution

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