This paper solves the open problem for an elliptical matrix variate version of the well known univariate Birnbaum and Saunders distribution. A generalisation based on a matrix transformation, instead of the independent element by element representation, was elusive in literature since the Gaussian univariate version was proposed in 1969. New results on linear structures were needed to derived the matrix variate distribution. A number of special cases are studied and some basic properties are found.

中文翻译：

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椭圆模型下的矩阵变量 Birnbaum-Saunders 分布

本文解决了众所周知的单变量伯恩鲍姆和桑德斯分布的椭圆矩阵变量版本的开放问题。自 1969 年提出高斯单变量版本以来，基于矩阵变换而不是独立元素逐元素表示的泛化在文献中难以捉摸。需要关于线性结构的新结果来推导矩阵变量分布。研究了许多特殊情况并发现了一些基本属性。