In this note, we investigate the non-identifiability of the multivariate unified skew-normal distribution under permutation of its latent variables. We show that the non-identifiability issue also holds with other parametrizations and extends to the family of unified skew-elliptical distributions and more generally to selection distibutions. We provide several suggestions to make the unified skew-normal model identifiable and describe various sub-models that are identifiable.

翻译：在本文中，我们研究了多元非标准化偏态正态分布在其潜变量排列置换下的不可辨识性问题。我们证明了不可辨识性问题也适用于其他参数化形式，并扩展到了统一偏椭圆分布族和更一般的选择分布。我们提出了多种建议以使统一偏态正态模型具有可辨识性，并描述了几个可辨识子模型。