Antonella Capitanio

Bio: Antonella Capitanio is an academic researcher from University of Bologna. The author has contributed to research in topics: Skew normal distribution & Multivariate statistics. The author has an hindex of 9, co-authored 13 publications receiving 4772 citations. Previous affiliations of Antonella Capitanio include University of Padua.

Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution

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.

Distributions generated by perturbation of symmetry with emphasis on a multivariate skew $t$ distribution

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.

Statistical applications of the multivariate skew normal distribution

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.

Statistical applications of the multivariate skew-normal distribution

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.

The Skew-Normal and Related Families

Abstract: Preface 1. Modulation of symmetric densities 2. The skew-normal distribution: probability 3. The skew-normal distribution: statistics 4. Heavy and adaptive tails 5. The multivariate skew-normal distribution 6. Skew-elliptical distributions 7. Further extensions and other directions 8. Application-oriented work Appendices References.

Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations

Abstract: Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged.

Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution

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.

Distributions generated by perturbation of symmetry with emphasis on a multivariate skew $t$ distribution

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.

Continuous Multivariate Distributions

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