Having only two parameters, the Gamma-Lindley distribution does not provide enough flexibility for analyzing different types of lifetime data. From this perspective, in order to further enhance its flexibility, we set forward in this paper a new class of distributions named Generalized Gamma-Lindley distribution with four parameters. Its construction is based on certain mixtures of Gamma and Lindley distributions. The truncated moment, as a characterization method, has drawn a little attention in the statistical literature over the great popularity of the classical methods. We attempt to prove that the Generalized Gamma-Lindley distribution is characterized by its truncated moment of the first order statistics. This method rests upon finding a survival function of a distribution, that is a solution of a first order differential equation. This characterization includes as special cases: Gamma, Lindley, Exponential, Gamma-Lindley and Weighted Lindley distributions. Finally, a simulation study is performed to help the reader check whether the available data follow the underlying distribution.

中文翻译：

---

利用截断阶数统计量刻画广义Gamma-Lindley分布

Gamma-Lindley分布只有两个参数，不能为分析不同类型的寿命数据提供足够的灵活性。从这个角度出发，为了进一步增强其灵活性，我们在本文中提出了一种新的分布类型，称为具有四个参数的广义Gamma-Lindley分布。它的构造基于Gamma和Lindley分布的某些混合。截断矩作为一种表征方法，已经在统计文献中引起了对经典方法的广泛关注的一点关注。我们试图证明广义Gamma-Lindley分布的特征在于其一阶统计量的截断矩。该方法基于找到分布的生存函数，即一阶微分方程的解。此特征包括特殊情况：Gamma，Lindley，指数，Gamma-Lindley和加权Lindley分布。最后，进行模拟研究以帮助读者检查可用数据是否遵循基本分布。