论文标题
多元正常分布的连续混合物的配方
A formulation for continuous mixtures of multivariate normal distributions
论文作者
论文摘要
文献中长期以来以正常变量的连续混合物的形式存在几种制剂，其中混合变量在均值或方差上或在多变量正常变量的均值和方差上作用，通过将这些基本成分的性质从常数变为随机数量。最近，已经引入了其他混合型结构，其中混合操作运行的核心随机分量不一定是正常的。本工作的主要目的是证明许多现有的构造可以由使用两个单变量随机变量混合正常变量的公式包含。对于此公式，我们得出了各种一般特性。在拟议的框架内，制定新的参数家族的建议也更简单，我们提供了一些这样的情况。同时，博览会对普通混合物的主题进行了审查。
Several formulations have long existed in the literature in the form of continuous mixtures of normal variables where a mixing variable operates on the mean or on the variance or on both the mean and the variance of a multivariate normal variable, by changing the nature of these basic constituents from constants to random quantities. More recently, other mixture-type constructions have been introduced, where the core random component, on which the mixing operation operates, is not necessarily normal. The main aim of the present work is to show that many existing constructions can be encompassed by a formulation where normal variables are mixed using two univariate random variables. For this formulation, we derive various general properties. Within the proposed framework, it is also simpler to formulate new proposals of parametric families and we provide a few such instances. At the same time, the exposition provides a review of the theme of normal mixtures.
