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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Empirical Bayes and Hierarchical Bayes Estimation of Skew Normal Populations
TL;DR: This article developed empirical and hierarchical Bayesian methodologies for the skew normal populations through the EM algorithm and the Gibbs sampler, and a general concept of skewness to the normal distribution is considered throughout.
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Nonparametric Bayesian modelling using skewed Dirichlet processes
TL;DR: In this article, a new class of discrete random probability measures that extend the definition of Dirichlet process (DP) by explicitly incorporating skewness is introduced, where asymmetry is controlled by a single parameter in such a way that symmetric DPs are obtained as a special case of the general construction.
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The tail mean–variance optimal portfolio selection under generalized skew-elliptical distribution
TL;DR: In this paper, the authors proposed the Tail Mean-Variance (TMV) criterion based on the two measures of risk, i.e., the Tail Conditional Expectation (TCE) and Tail Variance (TV) under Generalized Skew-Elliptical (GSE) distribution, and used a convex optimization approach for the TMV optimization problem under the GSE distribution.
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Statistical analysis of heat waves in the state of victoria in australia
TL;DR: In this article, the daily maximum temperatures at ten selected stations are studied and an auto-regressive integrated moving-average model is used to prewhiten the time series and the number of mixture components is effectively determined by an innovative penalisation procedure.
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EM algorithm using overparameterization for the multivariate skew-normal distribution
TL;DR: The proposed EM algorithms can be regarded as an accelerated version with momentum of a recently proposed EM algorithm, which allows the construction of an efficient EM algorithm in a closed form, which can be extended to a mixture of multivariate skew-normal distributions.
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.
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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.