A new method for generalizing the Lindley distribution, by increasing the number of mixed models is presented formally. This generalized model, which is called the generalized Lindley of integer order, encompasses the exponential and the usual Lindley distributions as special cases when the order of the model is fixed to be one and two, respectively. The moments, the variance, the moment generating function, and the failure rate function of the initiated model are extracted. Estimation of the underlying parameters by the moment and the maximum likelihood methods are acquired. The maximum likelihood estimation for the right censored data has also been discussed. In a simulation running for various orders and censoring rates, efficiency of the maximum likelihood estimator has been explored. The introduced model has ultimately been fitted to two real data sets to emphasize its application.

中文翻译：

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一种新的灵活广义 Lindley 模型：性质、估计和应用

正式提出了一种通过增加混合模型的数量来泛化 Lindley 分布的新方法。当模型的阶数分别固定为 1 和 2 时，这种广义模型称为整数阶广义 Lindley 分布，它包含指数分布和通常的 Lindley 分布作为特殊情况。提取初始模型的矩、方差、矩生成函数和失效率函数。通过矩估计基本参数和最大似然方法获得。还讨论了右删失数据的最大似然估计。在针对各种订单和审查率运行的模拟中，已经探索了最大似然估计器的效率。