Multimatricvariate and Multimatrix Variate Distributions Based on Elliptically Contoured Laws under Real Normed Division Algebras

Document Type : Original Article

Authors
1 Facultad de Zootecnia y Ecología, Universidad Autónoma de Chihuahua, Chihuahua, México.
2 University of Medellin, Faculty of Basic Sciences, Carrera 87 No.30-65, Medellin, Colombia.
10.22034/jirss.2025.2042155.1078
Abstract
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.
Keywords
Subjects

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Volume 23, Issue 2
December 2024
Pages 35-67

  • Receive Date 28 September 2024
  • Revise Date 27 January 2025
  • Accept Date 18 February 2025