Probabilities in multimatrix variate distributions: an application in SARS-CoV-2

Abstract

Recently the termed \emph{multimatrix variate distributions} were proposed in \citet{dgcl:24a} as an alternative for univariate and vector variate copulas. The distributions are based on sample probabilistic dependent elliptically countered models and most of them are also invariant under this family of laws. Despite a large of results on matrix variate distributions since the last 70 years, the spherical multimatrix distributions and the associated probabilities on hyper cones can be computable. The multiple probabilities are set in terms of recurrent integrations allowing several matrix computation a feasible task. An application of the emerging probabilities is placed into a dynamic molecular docking in the SARS-CoV-2 main protease. Finally, integration over multimatrix Wishart distribution provides a simplification of a complex kernel integral in elliptical models under real normed division algebras and the solution was applied in elliptical affine shape theory.