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.
