Bayesian modeling using a class of bimodal skew-elliptical distributions
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Date
2009
Journal Title
Journal ISSN
Volume Title
Publisher
ELSEVIER SCIENCE BV
Abstract
We consider Bayesian inference using an extension of the family of skew-elliptical distributions studied by Azzalini [1985. A class of distributions which includes the normal ones. Scand. J. Statist. Theory and Applications 12 (2), 171-178]. This new class is referred to as bimodal skew-elliptical (BSE) distributions. The elements of the BSE class can take quite different forms. In particular, they can adopt both uni- and bimodal shapes. The bimodal case behaves similarly to mixtures of two symmetric distributions and we compare inference under the BSE family with the specific case of mixtures of two normal distributions. We study the main properties of the general class and illustrate its applications to two problems involving density estimation and linear regression. (C) 2008 Elsevier B.V. All rights reserved.
Description
Keywords
Bimodality, Density estimation, Linear regression, Skew-normal distribution, Stochastic representation, SYMMETRIC DISTRIBUTIONS, REPRESENTATION, INFERENCE