A General Class of Multivariate Skew-Elliptical Distributions
Márcia D. Branco,Dipak K. Dey +1 more
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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
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Portfolio separation properties of the skew-elliptical distributions, with generalizations
TL;DR: In this article, the two-fund separation property of the elliptical distributions is extended to the skew-elliptical case by adding a number of funds equaling the rank of the skewness matrix.
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A variational Bayesian approach for inverse problems with skew-t error distributions
TL;DR: A novel robust Bayesian approach to inverse problems with data errors following a skew-t distribution is developed and a variational type algorithm is proposed by minimizing the Kullback-Leibler divergence between the true posterior distribution and a separable approximation.
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Moments of scale mixtures of skew-normal distributions and their quadratic forms
Hyoung-Moon Kim,Chiwhan Kim +1 more
TL;DR: In this article, the first moments of scale mixtures of skew-normal distributions allowing for scale parameters were derived and the first two moments of their quadratic forms were obtained using those moments.
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A note on bias reduction of maximum likelihood estimates for the scalar skew t distribution
TL;DR: In this article, it was shown that the modified score function is always finite, considering the degrees of freedom as known and greater than or equal to 2, and that the maximum likelihood estimator of the shape parameter is also always finite.
Posted Content
On moments of folded and doubly truncated multivariate extended skew-normal distributions
TL;DR: In this paper, the authors developed recurrence relations for integrals that relate the density of multivariate extended skew-normal (ESN) distribution, including the well-known skew normal (SN) distribution introduced by Azzalini and Dalla-Valle (1996) and the popular multivariate normal distribution.
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.