The multivariate skew-normal distribution
Adelchi Azzalini,A. Dalla Valle +1 more
TLDR
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.Abstract:
SUMMARY The paper extends earlier work on the so-called skew-normal distribution, a family of distributions including the normal, but with an extra parameter to regulate skewness. The present work introduces a multivariate parametric family such that the marginal densities are scalar skew-normal, and studies its properties, with special emphasis on the bivariate case.read more
Citations
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Journal ArticleDOI
Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution
TL;DR: In this paper, a fairly 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.
Journal ArticleDOI
Distributions generated by perturbation of symmetry with emphasis on a multivariate skew $t$ distribution
TL;DR: 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.
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.
OtherDOI
Continuous Multivariate Distributions
TL;DR: In this article, the authors present a concise review of developments on various continuous multivariate distributions and present some basic definitions and notations, and present several important continuous multi-dimensional distributions and their significant properties and characteristics.
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.
References
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Formulation and estimation of stochastic frontier production function models
TL;DR: In this paper, the authors define the disturbance term as the sum of symmetric normal and (negative) half-normal random variables, and consider various aspects of maximum-likelihood estimation for the coefficients of a production function with an additive disturbance term of this sort.
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Measures of multivariate skewness and kurtosis with applications
TL;DR: In this article, the authors developed measures of multivariate skewness and kurtosis by extending certain studies on robustness of the t statistic, and the asymptotic distributions of the measures for samples from a multivariate normal population are derived and a test for multivariate normality is proposed.
Journal Article
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.
Journal ArticleDOI
Further results on a class of distributions which includes the normal ones
TL;DR: In this paper, an ulteriore parametro di forma for escursione agli indici di asimmetria e curtosi is presented. Butte et al. presentati ulteriori risultati relativi ad una classe di funzioni di densita gia trattate in un altro lavoro dell'autore.
Book
An Introduction to Regression Graphics
R. Dennis Cook,Sanford Weisberg +1 more
TL;DR: Getting Started.