Matrix variate Birnbaum–Saunders distribution under elliptical models

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