Matrix variate Birnbaum-Saunders distribution under elliptical models

TL;DR

This paper extends the Birnbaum-Saunders distribution to matrix variate elliptical models, deriving new properties, special cases, and applying maximum likelihood estimation to real data with model comparison.

Contribution

It introduces a matrix variate elliptical version of the Birnbaum-Saunders distribution using a novel matrix transformation approach.

Findings

Derived the elliptical matrix variate Birnbaum-Saunders distribution.

Obtained maximum likelihood estimates for various models.

Compared models using a modified BIC criterion on real data.

Abstract

This paper derives the elliptical matrix variate version of the well known univariate Birnbaum and Saunders distribution. A generalisation based on a matrix transformation is proposed, instead of the independent element by element representation of the Gaussian univariate version of 1969. New results on Jacobians were needed to derived the matrix variate distribution. A number of special cases are studied and some basic properties are found. Finally, an example based on real data of two populations is provided. The maximum likelihood estimates are found for a number of matrix variate generalised Birnbaum-Saunders distributions based on Kotz models. A comparison with the Gaussian kernel is also given by using a modified BIC criterion.