In this paper, we generalize the Birnbaum-Saunders (BS) distribution by two ways. One is based on the mixture representation of BS distribution, and a flexible weight is adopted to describe the kurtosis of the distribution. The other way is based on the transformation property of BS distribution, and we incorporate a power parameter in the transformation to describe the skewness of the distribution. Then a four-parameter BS distribution including skewness and kurtosis parameters is induced by combining the two ways. The properties of these generalized BS distributions are investigated. Then, the expectation maximization (EM) algorithm is proposed to estimate the parameters. Real data analysis is performed to illustrate the superiority of the generalized BS distributions. Finally, some potential generalizations are discussed.

中文翻译：

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一类用于可靠性建模的广义 Birnbaum-Saunders 分布

在本文中，我们通过两种方式概括了 Birnbaum-Saunders (BS) 分布。一种是基于BS分布的混合表示，采用灵活的权重来描述分布的峰态。另一种方法是基于 BS 分布的变换特性，我们在变换中加入一个功率参数来描述分布的偏度。然后将这两种方法结合起来，得到包括偏度和峰态参数的四参数 BS 分布。研究了这些广义 BS 分布的特性。然后，提出了期望最大化（EM）算法来估计参数。进行实际数据分析以说明广义 BS 分布的优越性。最后，讨论了一些潜在的概括。