The Birnbaum–Saunders (BS) distribution, introduced in 1969, is a popular univariate fatigue life distribution which has been widely used to model right-skewed lifetime and reliability data. In this paper, a new class of generalized multivariate BS distributions is proposed based on mean-variance mixture models to accommodate strongly skewed and heavy tailed multivariate lifetime data. Some special cases of this class as well as their properties are then discussed. We present a hierarchical representation which facilitates an efficient EM-type algorithm for the computation of maximum likelihood estimates. Empirical results from a simulation study and real data analyses show that this class of distributions outperforms many existing extensions of the BS distribution in modeling lifetime data.

1969年推出的Birnbaum-Saunders（BS）分布是一种流行的单变量疲劳寿命分布，已广泛用于对右偏寿命和可靠性数据进行建模。本文基于均值-方差混合模型，提出了一类新的广义多元BS分布，以适应严重偏斜和重尾的多元寿命数据。然后讨论此类的一些特殊情况及其属性。我们提出了一种分层表示形式，它有助于为最大似然估计的计算提供一种有效的EM类型算法。来自仿真研究和实际数据分析的经验结果表明，在对生命周期数据进行建模时，此类分布优于BS分布的许多现有扩展。