Bayesian modelling with skew-elliptical distributions

Abstract

The dissertation is devoted to modelling with a new class of multivariate skew elliptical distributions.  This family of distributions extends the elliptical ones by the addition of a vector of shape parameters.  It contains the multivariate skew normal, skew Student’s t and skew Cauchy as special cases.

Detailed exploration is confined to the case of the univariate skew normal distribution.  In particular, salient properties of the density are studied and comparisons are drawn with alternative skew normal proposals.  Applications considered include linear regression, variance components and survival models.  Bayesian analysis with these models are shown to be easily accomplished through the use of the Gibbs sampler.  The latter proves very straightforward to specify distributionally and to implement computationally.  Numerical examples show that skew normal modelling is a viable competitor to the celebrated normal theory methods.

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