椭圆模型下的矩阵变量Birnbaum-Saunders分布
Matrix variate Birnbaum-Saunders distribution under elliptical models
摘要：
本文导出了著名的一元Birnbaum和Saunders分布的椭圆矩阵变量形式。提出了一种基于矩阵变换的推广，而不是1969年的高斯单变量版本的独立元素表示。需要雅可比矩阵的新结果来导出矩阵变量分布。研究了一些特殊情况，发现了一些基本性质，最后给出了基于两个总体真实数据的例子。基于Kotz模型，给出了矩阵变量广义Birnbaum-Saunders分布的最大似然估计.与高斯核的比较也给出了通过使用修改的BIC准则。
英文摘要：
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.
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