Mathematical Sciences: Models and Structures of Multivariate Distributions

大量的单变量分布有时已被深入研究，用于数据的统计分析；其他分布来自自然概率或物理考虑，来自统计性质，或作为限制分布。大多数知名的分布都有多种出现方式。虽然单变量分布提供了关于单个测量的信息，但它们不能促进测量之间关系的研究。在物理、生物和经济科学的许多情况下，正是这些关系令人感兴趣，因此需要多元分布。本建议的目标是有助于理解众所周知的单变量理论的多变量版本，重点是生命分布。这个主题是特别及时的，因为最近计算和计算机图形学能力的增加使得多元分布的使用更加广泛实用。在将许多多变量家族统一为内聚单元的基础结构方面，现在对多变量模型的理解特别差。多变量分布的有意义的推导可以阐明在不同的应用程序中使用哪些模型。这项研究的一个结果是，描述多变量数据的灵活模型将变得可用。

The large number of univariate distributions that have been thoroughly studied sometimes have been developed for use in statistical analyses of data; other distributions arise from natural probabilistic or physical considerations, from statistical properties, or as limiting distributions. Most of the well-known distributions arise in more than one way. Although univariate distributions provide information about individual measurements, they cannot facilitate studies of relationships between measurements. In many situations in the physical, biological, and economic sciences, it is just these relationships that are of interest, for which multivariate distributions are required. The goal of this proposal is to contribute to the understanding of multivariate versions of the well known univariate theory, with emphasis on life distributions. This subject is particularly timely because recent increases in computational and computer graphics capabiliteies have made the use of multivariate distributions much more broadly practical. Multivariate models are now particularly poorly understood in terms of underlying structures that unite many multivariate families into cohesive units. Meaningful derivations of multivariate distributions can shed light on which models to use in different applications. A consequence of this research is that flexible models useful in describing multivariate data will become available.