摘要:
随机向量的$t$分布属于椭球等高分布族, 然而, 它是对称分布. 在许多诸如经济学、生理学、社会学等领域中, 有时回归模型中的随机误差不再满足对称性, 通常表现出高度的偏态性(skewness). 于是就有了偏态椭球等高分布族. 本文在已有的多元偏态$t$分布的基础上, 着重研究它的分布性质, 包括线性组合分布、边缘分布、条件分布及各阶矩.
Abstract:
Multivariate $t$ distributions belong to elliptically contoured distributions. However, they are symmetric. In many fields such as economics, psychology and sociology, sometimes error structures in a regression type models no longer satisfy symmetric property. Generally there is a presence of high skewness. Therefore, multivariate skew elliptical distributions have been developed. In this paper, properties about known family of multivariate skew $t$ distributions are stressed. Linear transformations, marginal and conditional density are given. Also moments are derived.
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