This paper proposes famillies of multimatricvariate and multimatrix variate distributions based on elliptically contoured laws in the context of real normed division algebras. The work allows to answer the following inference problems about random matrix variate distributions: 1) Modeling of two or more probabilistically dependent random variables in all possible combinations whether univariate, vector and matrix simultaneously. 2) Expected marginal distributions under independence and joint estimation of models under likelihood functions of dependent samples. 3) Definition of a likelihood function for dependent samples in the mentioned random dimensions and under real normed division algebras. The corresponding real distributions are alternative approaches to the existing univariate and vector variate copulas, with the additional advantages previously listed. An application for quaternionic algebra is illustrated by a computable dependent sample joint distribution for landmark data emerged from shape theory.

翻译：本文提出了基于实范数除代数框架下椭圆等高律的多矩阵变量与多矩阵变量分布族。该工作能够解决关于随机矩阵变量分布的以下推断问题：1）对两个或更多概率相依随机变量在所有可能组合（包括单变量、向量和矩阵同时存在的情形）中进行建模；2）在独立假设下的期望边际分布，以及基于相依样本似然函数的模型联合估计；3）在所述随机维度下，基于实范数除代数定义相依样本的似然函数。相应的实分布为现有单变量和向量变量联结函数提供了替代方法，并具备前述的额外优势。通过形状理论中地标数据的可计算相依样本联合分布，展示了四元数代数的一个应用实例。