A General Class of Multivariate Skew-Elliptical Distributions
Márcia D. Branco,Dipak K. Dey +1 more
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TLDR
In this article, a general class of multivariate skew-elliptical distributions is proposed, which contains the multivariate normal, Student's t, exponential power, and Pearson type II, with an extra parameter to regulate skewness.About:
This article is published in Journal of Multivariate Analysis.The article was published on 2001-10-01 and is currently open access. It has received 629 citations till now. The article focuses on the topics: Elliptical distribution & Multivariate stable distribution.read more
Citations
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On Fisher information matrices and profile log-likelihood functions in generalized skew-elliptical models
Christophe Ley,Davy Paindaveine +1 more
TL;DR: In this article, it was shown that Fisher information matrices in the vicinity of symmetry are singular for Gaussian kernels only, and if the profile log-likelihood function for skewness always has a point of inflection in the direction of symmetry, the generalized skew-elliptical distribution considered is actually skew-(multi)normal.
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Skew-elliptical distributions with applications in risk theory
TL;DR: In this paper, the authors derived important properties of the well-known skew-elliptical (SE) distributions which was introduced in Azzalini and Capitanio (J R Stat Soc Ser B (Stat Methodol) 65:367-389, 2003), and including the more familiar skew-normal, skew-student-t and skew-logistic distributions.
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Mean mixtures of normal distributions: properties, inference and application
TL;DR: In this article, a general class of skewed distributions based on mean mixtures of normal distributions, which includes the skew normal distribution as a special case, are derived, and estimates of the model parameters are first obtained by the method of moments.
References
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MonographDOI
Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance
TL;DR: In this paper, the authors introduce sample path properties such as boundedness, continuity, and oscillations, as well as integrability, and absolute continuity of the path in the real line.
Book
Symmetric Multivariate and Related Distributions
TL;DR: In this article, the authors define marginal distributions, moments and density marginal distributions moments density the relationship between (phi and f) conditional distributions properties of elliptically symmetric distributions mixtures of normal distributions robust statistics and regression model robust statistics regression model log-elliptical and additive logistic elliptical distributions multivariate log elliptical distribution additive logistics elliptical distribution complex elliptical symmetric distribution.
Journal ArticleDOI
The multivariate skew-normal distribution
Adelchi Azzalini,A. Dalla Valle +1 more
TL;DR: In this article, a multivariate parametric family such that the marginal densities are scalar skew-normal is introduced, and its properties are studied with special emphasis on the bivariate case.
Journal ArticleDOI
Statistical applications of the multivariate skew normal distribution
TL;DR: Azzalini and Dalla Valle as discussed by the authors have discussed the multivariate skew normal distribution which extends the class of normal distributions by the addition of a shape parameter, and a further extension is described which introduces a skewing factor of an elliptical density.
Journal ArticleDOI
Statistical applications of the multivariate skew-normal distribution
TL;DR: Azzalini and Dalla Valle as mentioned in this paper have recently discussed the multivariate skew-normal distribution which extends the class of normal distributions by the addition of a shape parameter.