Journal ArticleDOI
Distributions generated by perturbation of symmetry with emphasis on a multivariate skew $t$ distribution
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In this paper, a general procedure is studied to perturb a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities.Abstract:
A fairly general procedure is studied to perturbate a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities. The approach is general enough to encompass a number of recent proposals in the literature, variously related to the skew normal distribution. The special case of skew elliptical densities is examined in detail, establishing connections with existing similar work. The final part of the paper specializes further to a form of multivariate skew $t$ density. Likelihood inference for this distribution is examined, and it is illustrated with numerical examples.read more
Citations
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Journal ArticleDOI
The Skew-normal Distribution and Related Multivariate Families.
TL;DR: In this paper, the authors provide an introductory overview of a portion of distribution theory which is currently under intense development and illustrate connections with various areas of application, including selective sampling, models for compositional data, robust methods, some problems in econometrics, non-linear time series, especially in connection with financial data, and more.
Book
The Skew-Normal and Related Families
TL;DR: This comprehensive treatment, blending theory and practice, will be the standard resource for statisticians and applied researchers, and Assuming only basic knowledge of (non-measure-theoretic) probability and statistical inference, the book is accessible to the wide range of researchers who use statistical modelling techniques.
Book ChapterDOI
Automated high-dimensional flow cytometric data analysis
Saumyadipta Pyne,Xinli Hu,Kui Wang,Elizabeth J. Rossin,Tsung-I Lin,Lisa M. Maier,Clare Baecher-Allan,Geoffrey J. McLachlan,Pablo Tamayo,David A. Hafler,Philip L. De Jager,Jill P. Mesirov +11 more
TL;DR: This work presents a direct multivariate finite mixture modeling approach, using skew and heavy-tailed distributions, to address the complexities of flow cytometric analysis and to deal with high-dimensional cytometric data without the need for projection or transformation.
Journal ArticleDOI
The Generalized Hyperbolic Skew Student’s t-Distribution
Kjersti Aas,Ingrid Hobæk Haff +1 more
TL;DR: In this article, a special case of the generalized hyperbolic (GH) family, called the GH skew Student's t-distribution, has been proposed, which has the important property that one tail has polynomial and the other exponential behavior.
Posted Content
The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map
William T. Shaw,I. R. C. Buckley +1 more
TL;DR: In this article, a technique for introducing skewness or kurtosis into a symmetric or other distribution is proposed, based on a "transmutation map" which is the functional composition of the cumulative distribution function of one distribution with the inverse cumulative distribution (quantile) function of another.
References
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A class of distributions which includes the normal ones
TL;DR: In this paper, a nouvelle classe de fonctions de densite dependant du parametre de forme λ, telles que λ=0 corresponde a la densite normale standard.
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Journal ArticleDOI
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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.
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