Kernel Oriented Generator Distribution

TL;DR

This paper introduces a unified method to generate matrix variate distributions using kernel functions and an unknown generator component, expanding the family of matrix variate distributions with new properties and special cases.

Contribution

It proposes a novel unified methodology for generating matrix variate distributions by combining kernels with a generator component, including derivation of their statistical properties.

Findings

Derived properties of the new distribution family.

Included special cases like the matrix variate Kummer beta distribution.

Discussed potential extensions and applications.

Abstract

Matrix variate beta (MVB) distributions are used in different fields of hypothesis testing, multivariate correlation analysis, zero regression, canonical correlation analysis and etc. In this approach a unified methodology is proposed to generate matrix variate distributions by combining the kernel of MVB distributions of different types with an unknown Borel measurable function of trace operator over matrix space, called generator component. The latter component is a principal element of these newly defined generator type matrix variate distributions. The matrix variate Kummer beta distribution is amongst others a special case. Several statistical properties of this newly defined family of distributions are derived. In the conclusion other extensions and developments are discussed.