Matrix Kummer-Pearson VII Relation and its Application in Affine Shape

TL;DR

This paper derives a matrix Kummer relation based on the Pearson VII matrix model, enabling exact inference in affine shape analysis by establishing a polynomial Pearson VII configuration density.

Contribution

It introduces a new matrix Kummer relation and applies it to shape theory, providing a solvable framework for affine shape inference.

Findings

Derived a matrix Kummer relation for Pearson VII matrix model

Established a polynomial Pearson VII configuration density

Enabled exact inference in affine shape analysis

Abstract

A case of the matrix Kummer relation of Herz (1955) based on the Pearson VII type matrix model is derived in this paper. As a consequence, the polynomial Pearson VII configuration density is obtained and this set the corresponding exact inference as a solvable aspect in shape theory.