Author
A. Dalla Valle
Bio: A. Dalla Valle is an academic researcher. The author has contributed to research in topics: Parametric family & Skewness. The author has an hindex of 1, co-authored 1 publications receiving 1369 citations.
Papers
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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.
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.
1,478 citations
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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.
Abstract: Summary. 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. The approach is sufficiently general to encompass some 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.
1,215 citations
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.
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.
1,174 citations
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.
Abstract: Azzalini and Dalla Valle have recently discussed the multivariate skew normal distribution which extends the class of normal distributions by the addition of a shape parameter. The first part of the present paper examines further probabilistic properties of the distribution, with special emphasis on aspects of statistical relevance. Inferential and other statistical issues are discussed in the following part, with applications to some multivariate statistics problems, illustrated by numerical examples. Finally, a further extension is described which introduces a skewing factor of an elliptical density.
1,130 citations
29 Sep 2014
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.
Abstract: In this article, we present a concise review of developments on various continuous multivariate distributions. We first present some basic definitions and notations. Then, we present several important continuous multivariate distributions and list their significant properties and characteristics.
Keywords:
generating function;
moments;
conditional distribution;
truncated distribution;
regression;
bivariate normal;
multivariate normal;
multivariate exponential;
multivariate gamma;
dirichlet;
inverted dirichlet;
liouville;
multivariate logistic;
multivariate pareto;
multivariate extreme value;
multivariate t;
wishart translated systems;
multivariate exponential families
1,106 citations
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.
Abstract: Azzalini & Dalla Valle (1996) have recently discussed the multivariate skew-normal distribution which extends the class of normal distributions by the addition of a shape parameter. The first part of the present paper examines further probabilistic properties of the distribution, with special emphasis on aspects of statistical relevance. Inferential and other statistical issues are discussed in the following part, with applications to some multivariate statistics problems, illustrated by numerical examples. Finally, a further extension is described which introduces a skewing factor of an elliptical density.
1,046 citations