Multimatricvariate distribution under elliptical models

TL;DR

This paper introduces a new family of multimatricvariate distributions based on elliptical models, generalizing bimatrix variate distributions, with properties, special cases, Jacobians, and an application to DNA time series data.

Contribution

It proposes the multimatricvariate distribution family, extending existing matrix variate models with new properties, Jacobians, and a real-world DNA data application.

Findings

Derived properties and special cases of the distributions.

Introduced two new Jacobians relevant to the area.

Applied the model to analyze time-dependent DNA data.

Abstract

A new family of matrix variate distributions indexed by elliptical models are proposed in this work. The so called \emph{multimatricvariate distributions} emerge as a generalization of the bimatrix variate distributions based on matrix variate gamma distributions and independence. Some properties and special cases of the multimatricvariate distributions are also derived. Two new interesting Jacobians in the area are also provided. Finally, an application for time dependent data of DNA molecules is studied.