Multimatrix variate distributions

TL;DR

This paper introduces multimatrix variate distributions, extending classical matrix variate distributions with invariant properties and diverse special cases, enabling flexible modeling and applications such as molecular docking.

Contribution

It proposes a new family of multimatrix variate distributions based on elliptical models, expanding the scope of distribution theory beyond independent models and copulas.

Findings

Distributions are invariant under the spherical family.

Includes diverse special cases and properties.

Application demonstrated in molecular docking for SARS-CoV-2.

Abstract

A new family of distributions indexed by the class of matrix variate contoured elliptically distribution is proposed as an extension of some bimatrix variate distributions. The termed \emph{multimatrix variate distributions} open new perspectives for the classical distribution theory, usually based on probabilistic independent models and preferred untested fitting laws. Most of the multimatrix models here derived are invariant under the spherical family, a fact that solves the testing and prior knowledge of the underlying distributions and elucidates the statistical methodology in contrasts with some weakness of current studies as copulas. The paper also includes a number of diverse special cases, properties and generalisations. The new joint distributions allows several unthinkable combinations for copulas, such as scalars, vectors and matrices, all of them adjustable to the required models of the experts. The proposed joint distributions are also easily computable, then several applications are plausible. In particular, an exhaustive example in molecular docking on SARS-CoV-2 presents the results on matrix dependent samples.