Skewing Around: Relationships Among Classes of Skewed Distributions

摘要

The relationships among normal hidden truncation models, closed skew normal families, fundamental skew normal families and extended skew normal families are explored. The models of Arnold and Beaver in (Test 11(1):7–54, 2002) include all of these absolutely continuous models. Slightly more general absolutely continuous models are available with the label of selection models in Arellano-Valle and Genton (Journal of Multivariate Analysis 96:93–116, 2005). The hidden truncation paradigm provides a convenient description of models that subsumes the full spectrum of these skewed models, including singular and absolutely continuous versions.