Mathematical Sciences: Models and Structures of MultivariateDistributions

研究了给定边际的多元统计分布问题。分布函数的Frechet界将通过施加额外的约束得到改进，例如相关性的特定值或联合分布具有对称性或单峰性的要求。将研究分布的各种排序和度量，特别是在严格递增的边际变换下的不变性的替代排序。用相对容易处理的多元分布来近似复杂多元分布的适宜性将被检验。将单变量分布扩展到更高维度的一些方法将被研究为独立基，表征，从伯努利或Urn模型中采样，激波模型和混合物。

The research concerns the topic of multivariate statistical distributions with given marginals. Frechet bounds for the distribution functions will be improved through the imposition of additional constraints such as a specific value for the correlation or the requirement that the joint distributions have symmetry or unimodality. Various orderings and measures for the distributions will be studied and, in particular, alternative orderings to invariance under strictly increasing marginal transformations. The suitability of approximations to complicated multivariate distributions by relatively tractable multivariate distributions will be examined. Some of the methods of extending univariate distributions to higher dimensions that will be studied are independent bases, characterizations, sampling from Bernoulli or Urn models, shock models and mixtures.