Multimatrix variate distributions

Document Type : Original Article

Authors

José A. Díaz-García ¹

Francisco J‎. ‎ Caro-Lopera ²

¹ Facultad de Zootecnia y Ecología, Universidad Autónoma de Chihuahua,Periférico Francisco R. Almada Km 1, Zootecnia, Chihuahua, 33820, Chihuahua, México

² Institute of Basic Sciences and Faculty of Engineering‎, ‎University of Medellin‎, ‎Carrera 87 No.30-65‎, ‎Medellin‎, ‎Antioquia‎, ‎Colombia

10.22067/smps.2026.94999.1050

Abstract

new family of distributions indexed by the class of matrix-variate elliptically contoured distributions is proposed‎, ‎extending several known bimatrix-variate models‎. ‎These multimatrix-variate distributions open new perspectives in classical distribution theory‎, ‎which is typically grounded in probabilistic independence assumptions and frequently relies on unverified fitting laws‎. ‎Most of the multimatrix models derived here are invariant under the spherical family‎, ‎a property that facilitates inference and reduces the need for prior specification of the underlying distributions‎. ‎This invariance clarifies the statistical methodology and addresses certain limitations present in existing approaches‎, ‎such as copula-based models‎. ‎The paper also presents a variety of special cases‎, ‎fundamental properties‎, ‎and generalizations‎. ‎The proposed joint distributions allow flexible combinations across scalars‎, ‎vectors‎, ‎and matrices‎, ‎making them adaptable to complex modeling requirements‎. ‎Moreover‎, ‎they are computationally tractable‎, ‎enabling a wide range of practical applications‎. ‎In particular‎, ‎we provide a comprehensive example in molecular docking for SARS-CoV-2‎, ‎illustrating the analysis of matrix-dependent samples.

Keywords

Bimatrix variate‎

‎Matricvariate‎

‎Matrix variate‎

‎Matrix variate elliptically contoured distributions‎

‎Random matrices

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