Mathematical Sciences: Models and Structures of Multivariate Distributions

大量的单变量分布， 经过彻底研究，有时已开发用于 数据的统计分析;其他分布来自 自然概率或物理考虑，从 统计特性，或极限分布。 大部分 众所周知的分布以不止一种方式出现。 虽然单变量分布提供了关于 个别测量，它们不能促进研究 测量之间的关系。 在许多情况下， 物理学、生物学和经济学， 关系是感兴趣的，对于多变量 分配是必需的。 本提案的目标是促进 了解多变量版本的众所周知的 单变量理论，重点是寿命分布。 这 这一主题特别及时，因为最近 计算和计算机图形能力已经使 多变量分布的使用更加广泛实用。 多变量模型现在特别缺乏了解， 将许多多元变量 把家庭变成有凝聚力的单位。 有意义的衍生 多变量分布可以说明要使用哪些模型 in different不同applications应用. 这项研究的结果是 在描述多变量数据时， 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.