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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A High-Dimensional Nonparametric Multivariate Test for Mean Vector
TL;DR: In this paper, a nonparametric test for the population mean vector of non-normal high-dimensional multivariate data was proposed, and the authors proved that the limiting null distribution of the proposed test is normal under mild conditions.
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Skewed distributions in finance and actuarial science: a review
TL;DR: A review of the use of the skew-normal distribution and its extensions in finance and actuarial science, highlighting known results as well as potential directions for future research is presented in this article.
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Asset pricing and portfolio selection based on the multivariate extended skew-Student-t distribution
TL;DR: The paper shows that the market model is non-linear in general and that the sensitivity of asset returns to return on the market portfolio is not the same as the conventional beta, although this measure does arise in special cases.
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mixsmsn: Fitting Finite Mixture of Scale Mixture of Skew-Normal Distributions
TL;DR: The R package mixsmsn as mentioned in this paper implements routines for maximum likelihood estimation via an expectation maximization EM-type algorithm in finite mixture models with components belonging to the class of scale mixtures of the skew-normal distribution.
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Data-generating process uncertainty: What difference does it make in portfolio decisions?
Jun Tu,Guofu Zhou,Guofu Zhou +2 more
TL;DR: In this article, a novel way to incorporate uncertainty about the data-generating process (DGP) uncertainty in making investment decisions is proposed, which leads to nontrivial changes in both parameter estimates and optimal portfolio weights, but the certainty-equivalent losses associated with ignoring fat tails are small.
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.