Iranian Statistical Society Journal of the Iranian Statistical Society 1726-4057 23 2 2024 12 01 Multimatricvariate and Multimatrix Variate Distributions Based on Elliptically Contoured Laws under Real Normed Division Algebras 35 67 721535 10.22034/jirss.2025.2042155.1078 EN Jose A. Diaz-Garcia Facultad de Zootecnia y Ecología, Universidad Autónoma de Chihuahua, Chihuahua, México. 0000-0001-5406-8789 Francisco J. Caro-Lopera University of Medellin, Faculty of Basic Sciences, Carrera 87 No.30-65, Medellin, Colombia. 0000-0001-5406-8789 Journal Article 2024 09 28 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. https://jirss.irstat.ir/article_721535_2cc0363a9df7ace39029e3e3a378db6e.pdf