In this paper, we first propose a new general method to introduce various lifetime distributions by choosing an appropriate kernel distribution. They have some characteristics in common with the well-known Birnbaum-Saunders distribution. Then, we choose the triangular distribution as a kernel model and construct the new distribution. This distribution has its support on the positive real axis and consists of two-pieces. We show that the newly defined distribution is in fact a generalized Birnbaum-Saunders distribution. It is mathematically tractable for studying its theoretical properties in detail. Different methods of estimation of parameters are proposed. The existence and uniqueness problem of the maximum likelihood estimation method is discussed. The performances of the estimators are evaluated through simulation studies. A real data fitting which compares it with the ordinary Birnbaum-Saunders, Laplace Birnbaum-Saunders and other some generalized Birnbaum-Saunders distributions is also given.

中文翻译：

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Laplace Birnbaum-Saunders 分布的替代方案

在本文中，我们首先提出了一种新的通用方法，通过选择适当的内核分布来引入各种生命周期分布。它们与著名的 Birnbaum-Saunders 分布有一些共同特征。然后，我们选择三角分布作为核模型并构造新的分布。该分布在正实轴上具有支撑，由两部分组成。我们表明，新定义的分布实际上是广义的 Birnbaum-Saunders 分布。它在数学上易于详细研究其理论性质。提出了不同的参数估计方法。讨论了最大似然估计方法的存在唯一性问题。通过模拟研究评估估计器的性能。