Distributions with Generalized Skewed Conditionals and Mixtures of Such Distributions

Abstract

Mixtures of skewed distributions (univariate and bivariate) provide flexible models. An alternative modeling approach involves distributions with skewed conditional distributions and mixtures of such distributions. We consider the interrelationships between such models. Examples are provided to show that several skewed distributions already considered in the literature can be viewed as having been constructed via a combination of mixing and skewing.

Keywords:

• Conditional specification
• Mixture distributions
• Skew normal distribution

Mathematics Subject Classification:

• Primary 62H05
• Secondary 60E05

Acknowledgments

We are grateful to an anonymous referee for helpful suggestions regarding the presentation of these results. We wish to thank the Universities of Cantabria and Castilla-La Mancha, and the Dirección General de Investigación Científica y Técnica (DGICYT) (projects DPI2002-04172-C04-02, BIA2005-07802-C02-01 and SEJ2004-02810), for partial support of this work.